시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

JOI 카레 매점은 매우 긴 난(인도의 납작한 빵)을 판매하는 것으로 유명하다. 난에는 $L$개의 맛이 있으며, 1번부터 $L$번까지 번호가 붙어 있다. 난 중에서 "JOI 스페셜 난"이 제일 인기가 있다. 길이가 $L$cm 이고, 왼쪽에서 $j-1$cm 부터 $j$cm 까지 부분에는 $j$번 ($1\le j \le L$) 맛으로 되어 있다.

$N$명의 사람이 JOI 카레 매점에 왔다. 그들의 취향은 다른 사람과 다르다. 구체적으로, $i$ 번째 ($1 \le i \le N$) 사람이 $j$번 ($1 \le j \le L$) 맛의 난을 먹었을 경우에는, 1 cm당 $V_{i, j}$의 행복도를 얻을 것이다.
그들은 하나의 JOI 스페셜 난을 주문했다. 그들은 난을 다음과 같은 방법으로 나누어 가질 것이다.

  1. $0 < X_1 < X_2 < \cdots < X_{N-1} < L$을 만족하는 $N-1$개의 분수 $X_1,\ \cdots,\ X_{N-1}$를 고른다.
  2. $N$개의 정수 $P_1,\ \cdots, \ P_N$을 고른다. 이는 $1, \ \cdots, \ N$의 순열이어야 한다.
  3. 각 $k$ ($1 \le k \le N-1$)에 대해서, 난을 $X_k$지점에서 자른다. 난은 $N$개의 조각으로 나누어질 것이다.
  4. 각 $k$ ($1 \le k \le N$)에 대해서, $P_k$번째 사람에게 $X_{k-1}$과 $X_k$ 사이의 조각을 준다. 우리는 $X_0$을 0, $X_N$을 $L$이라고 생각할 것이다.

우리는 난을 공평하게 나누고 싶다. 우리는 각 사람이 혼자 JOI 스페셜 난을 모두 먹었을 때 얻는 행복도의 $1/N$이상을 얻었을 경우, 분배 방식이 공평하다고 할 것이다.

$N$명의 사람의 선호가 주어졌을 때, 난을 공평하게 나누는 방법이 있는가를 출력하여라. 있는 경우, 난을 공평하게 나누는 방법에 대해 출력하여라.

입력

표준 입력에서 다음과 같은 형식으로 주어진다. 모든 수는 정수이다.

$N$ $L$

$V_{1,1}$ $V_{1, 2}$ $\cdots$ $V_{1, L}$

$\vdots$

$V_{N,1}$ $V_{N, 2}$ $\cdots$ $V_{N, L}$

출력

난을 공평하게 나누는 방법이 없다면, -1을 첫째 줄에 출력하여라. 공평하게 나눌 수 있다면, 나누는 방법을 나타내는 $N-1$개의 분수 $X_1,\ \cdots,\ X_{N-1}$과 $N$개의 정수 $P_1, \cdots, P_N$을 다음 형식으로 출력하여라.

$A_1$ $B_1$

$A_2$ $B_2$

$\vdots$

$A_{N-1}$ $B_{N-1}$

$P_1$ $P_2$ $\cdots$ $P_N$

$A_i$, $B_i$는 $X_i = \dfrac{A_i}{B_i}$ ($1 \le i \le N$)를 만족하는 정수 쌍이다. 이 정수는 출력 제한을 따라야 한다.

제한

입력 제한

  • $1 \le N \le 2000$.
  • $0 \le L \le 2000$.
  • $1 \le V_{i, j} \le 100\ 000$ ($1 \le i \le N,\ 1 \le j \le L$).

출력 제한

난을 공평한 방식으로 나눈 방법이 존재한다면, 출력은 다음 제한을 따라야 한다.

  • $1 \le B_i \le 1\ 000\ 000\ 000$. ($1 \le i \le N$)
  • $0 \le \dfrac{A_1}{B_1} < \dfrac{A_2}{B_2} \cdots < \dfrac{A_{N-1}}{B_{N-1}} < L$.
  • $P_1, \ \cdots, \ P_N$은 $1, \ \cdots, \ N$의 순열이다.
  • 분배에서, $i$번째 사람이 가지는 행복도의 양은 $\dfrac{V_{i, 1}+V_{i,2}+\cdots+V_{i,L}}{N}$ 이상 이어야 한다.

$A_i$와 $B_i$는 서로소일 필요는 없다.
아래 제한 하에서, 공평한 분배가 존재 할 경우 $1 \le B_i \le 1\ 000\ 000\ 000$을 만족하는 출력이 존재함을 증명할 수 있다.

예제 입력 1

2 5
2 7 1 8 2
3 1 4 1 5

예제 출력 1

14 5
2 1

이 예제에서, 모든 난을 먹었을 때, 첫째 사람은 2 + 7 + 1 + 8 + 2 = 20의 행복도를 가지고 둘째 사람은 3 + 1 + 4 + 1 + 5 = 14의 행복도를 가진다. 즉, 첫째 사람이 $\dfrac{20}{2} = 10$ 이상의 행복도를 가지고 둘째 사람이 $\dfrac{14}{2} = 7$ 이상의 행복도를 가지면, 분배는 공평하다.

난을 $\dfrac{14}{5}$에서 나누면, 첫째 사람은 $1 \times \dfrac{1}{5} + 8 + 2 = \dfrac{51}{5}$의 행복도를 얻고, 둘째 사람은 $3 + 1 + 4 \times \dfrac{4}{5} = \dfrac{36}{5}$의 행복도를 얻는다. 그러므로, 이것은 공평한 분배이다.

예제 입력 2

7 1
1
2
3
4
5
6
7

예제 출력 2

1 7
2 7
3 7
4 7
5 7
6 7
3 1 4 2 7 6 5

이 예제에서는 맛이 하나 뿐이다. 난을 크기가 같은 7개의 부분으로 자르면, $P_1, \ \cdots, \  P_N$과 관계 없이 분배가 공정하다.

예제 입력 3

5 3
2 3 1
1 1 1
2 2 1
1 2 2
1 2 1

예제 출력 3

15 28
35 28
50 28
70 28
3 1 5 2 4

$A_i$와 $B_i$가 서로소 일 필요는 없다. ($1 \le i \le N$)

[{"problem_id":"17670","problem_lang":"0","title":"\ub09c","description":"<p>JOI \uce74\ub808 \ub9e4\uc810\uc740 \ub9e4\uc6b0 \uae34 \ub09c(\uc778\ub3c4\uc758 \ub0a9\uc791\ud55c \ube75)\uc744 \ud310\ub9e4\ud558\ub294 \uac83\uc73c\ub85c \uc720\uba85\ud558\ub2e4. \ub09c\uc5d0\ub294 $L$\uac1c\uc758 \ub9db\uc774 \uc788\uc73c\uba70, 1\ubc88\ubd80\ud130 $L$\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc5b4 \uc788\ub2e4. \ub09c \uc911\uc5d0\uc11c &quot;JOI \uc2a4\ud398\uc15c \ub09c&quot;\uc774 \uc81c\uc77c \uc778\uae30\uac00 \uc788\ub2e4. \uae38\uc774\uac00 $L$cm \uc774\uace0, \uc67c\ucabd\uc5d0\uc11c $j-1$cm \ubd80\ud130 $j$cm \uae4c\uc9c0 \ubd80\ubd84\uc5d0\ub294 $j$\ubc88 ($1\\le j \\le L$) \ub9db\uc73c\ub85c \ub418\uc5b4 \uc788\ub2e4.<\/p>\r\n\r\n<p>$N$\uba85\uc758 \uc0ac\ub78c\uc774 JOI \uce74\ub808 \ub9e4\uc810\uc5d0 \uc654\ub2e4. \uadf8\ub4e4\uc758 \ucde8\ud5a5\uc740 \ub2e4\ub978 \uc0ac\ub78c\uacfc \ub2e4\ub974\ub2e4. \uad6c\uccb4\uc801\uc73c\ub85c, $i$ \ubc88\uc9f8 ($1 \\le i \\le N$) \uc0ac\ub78c\uc774 $j$\ubc88 ($1 \\le j \\le L$) \ub9db\uc758 \ub09c\uc744 \uba39\uc5c8\uc744 \uacbd\uc6b0\uc5d0\ub294, 1 cm\ub2f9 $V_{i, j}$\uc758 \ud589\ubcf5\ub3c4\ub97c \uc5bb\uc744 \uac83\uc774\ub2e4.<br \/>\r\n\uadf8\ub4e4\uc740 \ud558\ub098\uc758 JOI \uc2a4\ud398\uc15c \ub09c\uc744 \uc8fc\ubb38\ud588\ub2e4. \uadf8\ub4e4\uc740 \ub09c\uc744 \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \ub098\ub204\uc5b4 \uac00\uc9c8 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>$0 &lt; X_1 &lt; X_2 &lt; \\cdots &lt; X_{N-1} &lt; L$\uc744 \ub9cc\uc871\ud558\ub294 $N-1$\uac1c\uc758 \ubd84\uc218 $X_1,\\ \\cdots,\\ X_{N-1}$\ub97c \uace0\ub978\ub2e4.<\/li>\r\n\t<li>$N$\uac1c\uc758 \uc815\uc218 $P_1,\\ \\cdots, \\ P_N$\uc744 \uace0\ub978\ub2e4. \uc774\ub294 $1, \\ \\cdots, \\ N$\uc758 \uc21c\uc5f4\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\uac01 $k$ ($1 \\le k \\le N-1$)\uc5d0 \ub300\ud574\uc11c, \ub09c\uc744 $X_k$\uc9c0\uc810\uc5d0\uc11c \uc790\ub978\ub2e4. \ub09c\uc740 $N$\uac1c\uc758 \uc870\uac01\uc73c\ub85c \ub098\ub204\uc5b4\uc9c8 \uac83\uc774\ub2e4.<\/li>\r\n\t<li>\uac01 $k$ ($1 \\le k \\le N$)\uc5d0 \ub300\ud574\uc11c, $P_k$\ubc88\uc9f8 \uc0ac\ub78c\uc5d0\uac8c $X_{k-1}$\uacfc $X_k$ \uc0ac\uc774\uc758 \uc870\uac01\uc744 \uc900\ub2e4. \uc6b0\ub9ac\ub294 $X_0$\uc744 0, $X_N$\uc744 $L$\uc774\ub77c\uace0 \uc0dd\uac01\ud560 \uac83\uc774\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc6b0\ub9ac\ub294 \ub09c\uc744 \uacf5\ud3c9\ud558\uac8c \ub098\ub204\uace0 \uc2f6\ub2e4. \uc6b0\ub9ac\ub294 \uac01 \uc0ac\ub78c\uc774 \ud63c\uc790 JOI \uc2a4\ud398\uc15c \ub09c\uc744 \ubaa8\ub450 \uba39\uc5c8\uc744 \ub54c \uc5bb\ub294 \ud589\ubcf5\ub3c4\uc758 $1\/N$\uc774\uc0c1\uc744 \uc5bb\uc5c8\uc744 \uacbd\uc6b0, \ubd84\ubc30 \ubc29\uc2dd\uc774 <strong>\uacf5\ud3c9\ud558\ub2e4<\/strong>\uace0 \ud560 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>$N$\uba85\uc758 \uc0ac\ub78c\uc758 \uc120\ud638\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub09c\uc744 \uacf5\ud3c9\ud558\uac8c \ub098\ub204\ub294 \ubc29\ubc95\uc774 \uc788\ub294\uac00\ub97c \ucd9c\ub825\ud558\uc5ec\ub77c. \uc788\ub294 \uacbd\uc6b0, \ub09c\uc744 \uacf5\ud3c9\ud558\uac8c \ub098\ub204\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \ucd9c\ub825\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\ud45c\uc900 \uc785\ub825\uc5d0\uc11c \ub2e4\uc74c\uacfc \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ubaa8\ub4e0 \uc218\ub294 \uc815\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>$N$ $L$<\/p>\r\n\r\n<p>$V_{1,1}$ $V_{1, 2}$ $\\cdots$ $V_{1, L}$<\/p>\r\n\r\n<p>$\\vdots$<\/p>\r\n\r\n<p>$V_{N,1}$ $V_{N, 2}$ $\\cdots$ $V_{N, L}$<\/p>\r\n","output":"<p>\ub09c\uc744 \uacf5\ud3c9\ud558\uac8c \ub098\ub204\ub294 \ubc29\ubc95\uc774 \uc5c6\ub2e4\uba74, <tt>-1<\/tt>\uc744 \uccab\uc9f8 \uc904\uc5d0 \ucd9c\ub825\ud558\uc5ec\ub77c. \uacf5\ud3c9\ud558\uac8c \ub098\ub20c \uc218 \uc788\ub2e4\uba74, \ub098\ub204\ub294 \ubc29\ubc95\uc744 \ub098\ud0c0\ub0b4\ub294 $N-1$\uac1c\uc758 \ubd84\uc218 $X_1,\\ \\cdots,\\ X_{N-1}$\uacfc $N$\uac1c\uc758 \uc815\uc218 $P_1, \\cdots, P_N$\uc744 \ub2e4\uc74c \ud615\uc2dd\uc73c\ub85c \ucd9c\ub825\ud558\uc5ec\ub77c.<\/p>\r\n\r\n<p>$A_1$ $B_1$<\/p>\r\n\r\n<p>$A_2$ $B_2$<\/p>\r\n\r\n<p>$\\vdots$<\/p>\r\n\r\n<p>$A_{N-1}$ $B_{N-1}$<\/p>\r\n\r\n<p>$P_1$ $P_2$ $\\cdots$ $P_N$<\/p>\r\n\r\n<p>$A_i$, $B_i$\ub294 $X_i = \\dfrac{A_i}{B_i}$ ($1 \\le i \\le N$)\ub97c \ub9cc\uc871\ud558\ub294 \uc815\uc218 \uc30d\uc774\ub2e4. \uc774 \uc815\uc218\ub294 \ucd9c\ub825 \uc81c\ud55c\uc744 \ub530\ub77c\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\ud55c\uad6d\uc5b4","limit":"<p>\uc785\ub825 \uc81c\ud55c<\/p>\r\n\r\n<ul>\r\n\t<li>$1 \\le N \\le 2000$.<\/li>\r\n\t<li>$0 \\le L \\le 2000$.<\/li>\r\n\t<li>$1 \\le V_{i, j} \\le 100\\ 000$ ($1 \\le i \\le N,\\ 1 \\le j \\le L$).<\/li>\r\n<\/ul>\r\n\r\n<p>\ucd9c\ub825 \uc81c\ud55c<\/p>\r\n\r\n<p>\ub09c\uc744 \uacf5\ud3c9\ud55c \ubc29\uc2dd\uc73c\ub85c \ub098\ub208 \ubc29\ubc95\uc774 \uc874\uc7ac\ud55c\ub2e4\uba74, \ucd9c\ub825\uc740 \ub2e4\uc74c \uc81c\ud55c\uc744 \ub530\ub77c\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$1 \\le B_i \\le 1\\ 000\\ 000\\ 000$. ($1 \\le i \\le N$)<\/li>\r\n\t<li>$0 \\le \\dfrac{A_1}{B_1} &lt; \\dfrac{A_2}{B_2} \\cdots &lt; \\dfrac{A_{N-1}}{B_{N-1}} &lt; L$.<\/li>\r\n\t<li>$P_1, \\ \\cdots, \\ P_N$\uc740 $1, \\ \\cdots, \\ N$\uc758 \uc21c\uc5f4\uc774\ub2e4.<\/li>\r\n\t<li>\ubd84\ubc30\uc5d0\uc11c, $i$\ubc88\uc9f8 \uc0ac\ub78c\uc774 \uac00\uc9c0\ub294 \ud589\ubcf5\ub3c4\uc758 \uc591\uc740 $\\dfrac{V_{i, 1}+V_{i,2}+\\cdots+V_{i,L}}{N}$ \uc774\uc0c1 \uc774\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>$A_i$\uc640 $B_i$\ub294 \uc11c\ub85c\uc18c\uc77c \ud544\uc694\ub294 \uc5c6\ub2e4.<br \/>\r\n\uc544\ub798 \uc81c\ud55c \ud558\uc5d0\uc11c, \uacf5\ud3c9\ud55c \ubd84\ubc30\uac00 \uc874\uc7ac \ud560 \uacbd\uc6b0 $1 \\le B_i \\le 1\\ 000\\ 000\\ 000$\uc744 \ub9cc\uc871\ud558\ub294 \ucd9c\ub825\uc774 \uc874\uc7ac\ud568\uc744 \uc99d\uba85\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n","sample_explain_1":"<p>\uc774 \uc608\uc81c\uc5d0\uc11c, \ubaa8\ub4e0 \ub09c\uc744 \uba39\uc5c8\uc744 \ub54c, \uccab\uc9f8 \uc0ac\ub78c\uc740 2 + 7 + 1 + 8 + 2 = 20\uc758 \ud589\ubcf5\ub3c4\ub97c \uac00\uc9c0\uace0 \ub458\uc9f8 \uc0ac\ub78c\uc740 3 + 1 + 4 + 1 + 5 = 14\uc758 \ud589\ubcf5\ub3c4\ub97c \uac00\uc9c4\ub2e4. \uc989, \uccab\uc9f8 \uc0ac\ub78c\uc774 $\\dfrac{20}{2} = 10$ \uc774\uc0c1\uc758 \ud589\ubcf5\ub3c4\ub97c \uac00\uc9c0\uace0 \ub458\uc9f8 \uc0ac\ub78c\uc774 $\\dfrac{14}{2} = 7$ \uc774\uc0c1\uc758 \ud589\ubcf5\ub3c4\ub97c \uac00\uc9c0\uba74, \ubd84\ubc30\ub294 \uacf5\ud3c9\ud558\ub2e4.<\/p>\r\n\r\n<p>\ub09c\uc744 $\\dfrac{14}{5}$\uc5d0\uc11c \ub098\ub204\uba74, \uccab\uc9f8 \uc0ac\ub78c\uc740 $1 \\times \\dfrac{1}{5} + 8 + 2 = \\dfrac{51}{5}$\uc758 \ud589\ubcf5\ub3c4\ub97c \uc5bb\uace0, \ub458\uc9f8 \uc0ac\ub78c\uc740 $3 + 1 + 4 \\times \\dfrac{4}{5} = \\dfrac{36}{5}$\uc758 \ud589\ubcf5\ub3c4\ub97c \uc5bb\ub294\ub2e4. \uadf8\ub7ec\ubbc0\ub85c, \uc774\uac83\uc740 \uacf5\ud3c9\ud55c \ubd84\ubc30\uc774\ub2e4.<\/p>\r\n","sample_explain_2":"<p>\uc774 \uc608\uc81c\uc5d0\uc11c\ub294 \ub9db\uc774 \ud558\ub098 \ubfd0\uc774\ub2e4. \ub09c\uc744 \ud06c\uae30\uac00 \uac19\uc740 7\uac1c\uc758 \ubd80\ubd84\uc73c\ub85c \uc790\ub974\uba74, $P_1, \\ \\cdots, \\&nbsp; P_N$\uacfc \uad00\uacc4 \uc5c6\uc774 \ubd84\ubc30\uac00 \uacf5\uc815\ud558\ub2e4.<\/p>\r\n","sample_explain_3":"<p>$A_i$\uc640 $B_i$\uac00 \uc11c\ub85c\uc18c \uc77c \ud544\uc694\ub294 \uc5c6\ub2e4. ($1 \\le i \\le N$)<\/p>\r\n"},{"problem_id":"17670","problem_lang":"1","title":"Naan","description":"<p>JOI Curry Shop is famous for serving very long naans. They have L kinds of flavors, numbered from 1 through L, to flavor naans. &ldquo;JOI Special Naan&rdquo; is the most popular menu in the shop. The length of the naan is L cm. We define &ldquo;the position x&rdquo; as the position on the naan which is x cm distant from the left end of the naan. The segment between position j &minus; 1 and position j is flavored by flavor j (1 &le; j &le; L).<\/p>\r\n\r\n<p>N people came to JOI Curry Shop. Their preferences are different from each other. Specifically, when the i-th (1 &le; j &le; L) person eats naan with flavor j (1 &le; j &le; L), they will get happiness V<sub>i, j<\/sub> per 1 cm. They ordered only one JOI Special Naan. They will share the naan in the following manner:<\/p>\r\n\r\n<ol>\r\n\t<li>Choose N &minus; 1 rational numbers X<sub>1<\/sub>, . . . , X<sub>N&minus;1<\/sub> which satisfy 0 &lt; X<sub>1<\/sub> &lt; X<sub>2<\/sub> &lt; &middot; &middot; &middot; &lt; X<sub>N&minus;1<\/sub> &lt; L.<\/li>\r\n\t<li>Choose N integers P<sub>1<\/sub>, . . . , P<sub>N<\/sub> which form a permutation of 1, . . . , N.<\/li>\r\n\t<li>For each k (1 &le; k &le; N &minus; 1), cut the naan at the position X<sub>k<\/sub>. Thus, the naan will be separated into N pieces.<\/li>\r\n\t<li>For each k (1 &le; k &le; N), give the piece between the position X<sub>k&minus;1<\/sub> and position X<sub>k<\/sub> to the Pk-th person. We consider X<sub>0<\/sub> as 0 and X<sub>N<\/sub> as L.<\/li>\r\n<\/ol>\r\n\r\n<p>We want to distribute the naan fairly. We say a distribution is fair if each person gets happiness of more than or equal to 1 N of the amount of happiness they will get by eating the whole JOI Special Naan.<\/p>\r\n\r\n<p>Write a program which, given the information of preferences of N people, determines if it is possible to distribute the naan in a fair way, and if it is possible, finds such a fair way.<\/p>\r\n","input":"<p>Read the following data from the standard input. All the values in the input are integers.<\/p>\r\n\r\n<pre>\r\nN L\r\nV<sub>1,1<\/sub> V<sub>1,2<\/sub> &middot; &middot; &middot; V<sub>1,L<\/sub>\r\n.\r\n.\r\n.\r\nV<sub>N,1<\/sub> V<sub>N,2<\/sub> &middot; &middot; &middot; V<sub>N,L<\/sub><\/pre>\r\n","output":"<p>Write to the standard output. If it is impossible to distribute naan in a fair way, write &minus;1 in a line. If it is possible, output N &minus; 1 rational numbers X<sub>1<\/sub>, . . . , X<sub>N&minus;1<\/sub> and N integers P<sub>1<\/sub>, . . . , P<sub>N<\/sub> which represent a fair distribution, in the following format.<\/p>\r\n\r\n<pre>\r\nA<sub>1<\/sub> B<sub>1<\/sub>\r\nA<sub>2<\/sub> B<sub>2<\/sub>\r\n.\r\n.\r\n.\r\nA<sub>N&minus;1<\/sub> B<sub>N&minus;1<\/sub>\r\nP<sub>1<\/sub> P<sub>2<\/sub> &middot; &middot; &middot; P<sub>N<\/sub><\/pre>\r\n\r\n<p>A<sub>k<\/sub> and B<sub>k<\/sub> are a pair of integers which satisfies X<sub>k<\/sub> = A<sub>k<\/sub>\/B<sub>k<\/sub> (1 &le; k &le; N &minus; 1).<\/p>\r\n\r\n<p>If it is possible to distribute the naan in a fair way, the output must satisfy the following constraints:<\/p>\r\n\r\n<ul>\r\n\t<li>1 &le; B<sub>k<\/sub> &le; 1 000 000 000 (1 &le; k &le; N &minus; 1).<\/li>\r\n\t<li>0 &lt; A<sub>1<\/sub>\/B<sub>1<\/sub> &lt; A<sub>2<\/sub>\/B<sub>2<\/sub> &lt; &middot; &middot; &middot; &lt; A<sub>N&minus;1<\/sub>\/B<sub>N&minus;1<\/sub> &lt; L.<\/li>\r\n\t<li>P<sub>1<\/sub>, . . . , P<sub>N<\/sub> is a permutation of 1, . . . , N.<\/li>\r\n\t<li>In the distribution, the amount of happiness which i-th person will get is more than or equal to (V<sub>i,1<\/sub> + V<sub>i,2<\/sub> + &middot; &middot; &middot; + V<sub>i,L<\/sub>)\/N (1 &le; i &le; N).<\/li>\r\n<\/ul>\r\n\r\n<p>A<sub>k<\/sub> and B<sub>k<\/sub> are not necessary to be coprime (1 &le; k &le; N &minus; 1). Under the constraints of the input, it can be proved that if a fair distribution exists, there is a correct output which satisfies 1 &le; B<sub>k<\/sub> &le; 1 000 000 000 (1 &le; k &le; N &minus; 1).<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\uc601\uc5b4","limit":"<ul>\r\n\t<li>2 &le; N &le; 2 000.<\/li>\r\n\t<li>1 &le; L &le; 2 000.<\/li>\r\n\t<li>1 &le; V<sub>i, j<\/sub> &le; 100 000 (1 &le; i &le; N, 1 &le; j &le; L).<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>In this sample, the first person will get happiness of 2 + 7 + 1 + 8 + 2 = 20 when she eats the whole naan and the second person will get happiness of 3 + 1 + 4 + 1 + 5 = 14 when she eats the whole naan. Thus, if the first person gets happiness of more than or equal to 20\/2 = 10 and the second person gets happiness of more than or equal to 14\/2 = 7, the distribution is fair.<\/p>\r\n\r\n<p>If you cut the naan at the position 14\/5 , the first person will get happiness of 1 &times; 1\/5 + 8 + 2&nbsp; = 51\/5 and the second person will get happiness of 3 + 1 + 4 &times; 4\/5 = 36\/5. Hence, this is a fair distribution.<\/p>\r\n","sample_explain_2":"<p>In this sample, the naan has only one flavor. If you equally divide the naan into 7 pieces, the distribution will be fair, regardless of P<sub>1<\/sub>, . . . , P<sub>N<\/sub>.<\/p>\r\n","sample_explain_3":"<p>Note that A<sub>k<\/sub> and B<sub>k<\/sub> are not necessary to be coprime (1 &le; k &le; N &minus; 1).<\/p>\r\n"}]