시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB146641530928.638%

문제

1부터 N2까지 수가 지그재그 대각선 순서로 N*N 행렬에 채워져 있다. 아래 그림은 N=6일 때, 행렬의 모습이다.

1 2 6 7 15 16
3 5 8 14 17 26
4 9 13 18 25 27
10 12 19 24 28 33
11 20 23 29 32 34
21 22 30 31 35 36

토끼는 지금 1이 있는 칸에 있다. 토끼는 인접한 칸으로 점프할 수 있다. (위, 아래, 오른쪽, 왼쪽)

토끼가 점프한 방법이 주어졌을 때, 토끼가 방문한 칸에 있는 수의 합을 구하는 프로그램을 작성하시오. 같은 칸을 여러 번 방문할 경우에도, 방문할 때 마다 더해야 한다. 토끼가 행렬을 벗어나는 경우는 없다.

입력

첫째 줄에 N, K가 주어진다. (1 ≤ N ≤ 100,000, 1 ≤ K ≤ 300,000) N은 행렬의 크기, K는 토끼가 점프한 횟수이다.

둘째 줄에는 'U','D','L','R'로 이루어진 문자열이 주어진다. 이 문자열의 길이는 K이며, 토끼가 점프한 방향이다.

출력

첫째 줄에, 방문한 칸의 수의 합을 출력한다. 이 값은 32비트 정수를 넘을 수도 있다.

예제 입력 1

6 8
DDRRUULL

예제 출력 1

47

예제 입력 2

3 8
DDRRUULL

예제 출력 2

41

예제 입력 3

6 10
RRRRRDDDDD

예제 출력 3

203
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ZjRcdWM3NTggXHVhZTM4XHVjNzc0XHViMjk0IEtcdWM3NzRcdWJhNzAsIFx1ZDFhMFx1YjA3Y1x1YWMwMCBcdWM4MTBcdWQ1MDRcdWQ1NWMgXHViYzI5XHVkNWE1XHVjNzc0XHViMmU0LjxcL3A+XHJcbiIsIm91dHB1dCI6IjxwPlx1Y2NhYlx1YzlmOCBcdWM5MDRcdWM1ZDAsIFx1YmMyOVx1YmIzOFx1ZDU1YyBcdWNlNzhcdWM3NTggXHVjMjE4XHVjNzU4IFx1ZDU2OVx1Yzc0NCBcdWNkOWNcdWI4MjVcdWQ1NWNcdWIyZTQuIFx1Yzc3NCBcdWFjMTJcdWM3NDAgMzJcdWJlNDRcdWQyYjggXHVjODE1XHVjMjE4XHViOTdjIFx1YjExOFx1Yzc0NCBcdWMyMThcdWIzYzQgXHVjNzg4XHViMmU0LjxcL3A+XHJcbiIsImhpbnQiOiIiLCJvcmlnaW5hbCI6IjAiLCJodG1sX3RpdGxlIjoiMCIsInByb2JsZW1fbGFuZ190Y29kZSI6IktvcmVhbiJ9LHsicHJvYmxlbV9pZCI6IjMxMDEiLCJwcm9ibGVtX2xhbmciOiIxIiwidGl0bGUiOiJCUk9KRVZJIiwiZGVzY3JpcHRpb24iOiI8cD5BIE4mdGltZXM7TiBtYXRyaXggaXMgZmlsbGVkIHdpdGggbnVtYmVycyAxIHRvIE48c3VwPjI8XC9zdXA+LCBkaWFnb25hbGx5IGluIGEgemlnLXphZyBmYXNoaW9uLiBUaGUgaWxsdXN0cmF0aW9uIGJlbG93IHNob3dzIG51bWJlcnMgaW4gdGhlIG1hdHJpeCBmb3IgTiA9IDYuPFwvcD5cclxuXHJcbjxwPjxpbWcgYWx0PVwiXCIgc3JjPVwiXC91cGxvYWRcL2ltYWdlc1wvcmFiYml0LnBuZ1wiIHN0eWxlPVwiaGVpZ2h0OjE5NnB4OyB3aWR0aDoyMTNweFwiIFwvPjxcL3A+XHJcblxyXG48cD5UaGVyZSBpcyBhIHJhYmJpdCBpbiB0aGUgY2VsbCBjb250YWluaW5nIG51bWJlciAxLiBBIHJhYmJpdCBjYW4ganVtcCB0byBhIG5laWdoYm9yaW5nIGNlbGwgKHVwLCBkb3duLCBsZWZ0IG9yIHJpZ2h0KSBpZiB0aGF0IGNlbGwgZXhpc3RzLiZuYnNwOzxcL3A+XHJcblxyXG48cD5HaXZlbiBLIHZhbGlkIHJhYmJpdCBqdW1wcywgd3JpdGUgYSBwcm9ncmFtIHRoYXQgd2lsbCBjYWxjdWxhdGUgdGhlIHN1bSBvZiBudW1iZXJzIG9mIGFsbCBjZWxscyB0aGF0IHJhYmJpdCB2aXNpdGVkIChhZGQgdGhlIG51bWJlciB0byB0aGUgc3VtIGVhY2ggdGltZSByYWJiaXQgdmlzaXRzIHRoZSBzYW1lIGNlbGwpLiZuYnNwOzxcL3A+XHJcbiIsImlucHV0IjoiPHA+VGhlIGZpcnN0IGxpbmUgY29udGFpbnMgdHdvIGludGVnZXJzIE4gYW5kIEsgKDEgJmxlOyBOICZsZTsgMTAwMDAwLCAxICZsZTsgSyAmbGU7IDMwMDAwMCksIHRoZSBzaXplIG9mIHRoZSBtYXRyaXggYW5kIHRoZSBudW1iZXIgb2YgcmFiYml0IGp1bXBzLiZuYnNwOzxcL3A+XHJcblxyXG48cD5UaGUgc2Vjb25kIGxpbmUgY29udGFpbnMgYSBzZXF1ZW5jZSBvZiBLIGNoYXJhY3RlcnMgJiMzOTtVJiMzOTssICYjMzk7RCYjMzk7LCAmIzM5O0wmIzM5OyBhbmQgJiMzOTtSJiMzOTssIGRlc2NyaWJpbmcgdGhlIGRpcmVjdGlvbiBvZiBlYWNoIGp1bXAuIFRoZSBzZXF1ZW5jZSBvZiBqdW1wcyB3aWxsIG5vdCBsZWF2ZSB0aGUgbWF0cml4IGF0IGFueSBtb21lbnQuJm5ic3A7PFwvcD5cclxuIiwib3V0cHV0IjoiPHA+T3V0cHV0IG9uZSBpbnRlZ2VyLCB0aGUgc3VtIG9mIG51bWJlcnMgb24gdmlzaXRlZCBjZWxscy4mbmJzcDs8XC9wPlxyXG5cclxuPHA+Tm90ZTogVGhpcyBudW1iZXIgZG9lc24mIzM5O3QgYWx3YXlzIGZpdCBpbiAzMi1iaXQgaW50ZWdlciB0eXBlPFwvcD5cclxuIiwiaGludCI6IjxwPkNsYXJpZmljYXRpb24gZm9yIHRoZSBmaXJzdCBzYW1wbGU6IFRoZSByYWJiaXQgdmlzaXRzIGNlbGxzIDEsIDMsIDQsIDksIDEzLCA4LCA2LCAyIGFuZCAxLjxcL3A+XHJcblxyXG48cD5DbGFyaWZpY2F0aW9uIGZvciB0aGUgc2Vjb25kIHNhbXBsZTogVGhlIHJhYmJpdCB2aXNpdHMgY2VsbHMgMSwgMywgNCwgOCwgOSwgNywgNiwgMiBhbmQgMS48XC9wPlxyXG5cclxuPHA+Q2xhcmlmaWNhdGlvbiBmb3IgdGhlIHRoaXJkIHNhbXBsZTogVGhlIHJhYmJpdCB2aXNpdHMgY2VsbHMgMSwgMiwgNiwgNywgMTUsIDE2LCAyNiwgMjcsIDMzLCAzNCBhbmQgMzYuPFwvcD5cclxuIiwib3JpZ2luYWwiOiIxIiwiaHRtbF90aXRsZSI6IjAiLCJwcm9ibGVtX2xhbmdfdGNvZGUiOiJFbmdsaXNoIn1d