시간 제한메모리 제한제출정답맞힌 사람정답 비율
3 초 1024 MB264726337.725%

문제

출처: 윤찐빵

UDP 마을에 UDPC를 기념하는 벚꽃 축제가 열렸다! 벚꽃 축제는 $M$일간 열리며, 축제 장소에는 $N$그루의 나무가 일렬로 서 있다. 각 나무는 순서대로 $1$번부터 $N$번까지의 번호를 가진다. $i$번째 벚나무에는 축제의 $S_i$번째 날부터 $E_i$번째 날까지 벚꽃이 핀다. 벚꽃은 모여 있을수록 예쁘기 때문에 윤이, 달구, 포닉스는 가장 많은 벚나무가 일렬로 연속해서 핀 날에 꽃구경을 가려 한다. 어떤 날에 $a$번 나무부터 $b$번 나무까지 벚나무가 일렬로 연속해서 피어 있음은 어떤 날에 $a$번 나무부터 $b$번 나무까지 모두 벚꽃이 피어 있는 것을 의미한다. 또한, 어떤 날에 일렬로 연속해서 핀 벚나무의 개수는 이러한 $[a, b]$ 구간 중 길이 $b-a+1$의 최댓값이다. 축제를 잔뜩 기대 중인 세 마스코트를 위해 축제 기간 중 일렬로 연속해서 핀 벚나무 개수의 최댓값가장 많은 벚나무가 일렬로 연속해서 핀 날의 개수를 구해 보자!

입력

첫 번째 줄에 벚나무의 개수 $N$과 축제 기간 $M$이 공백으로 구분되어 주어진다. ($1\leq N\leq 10^5;1\leq M\leq 10^9$)

두 번째 줄부터 $N$줄에 걸쳐 $i+1$번째 줄에 $i$번째 벚나무에 벚꽃이 피는 기간을 나타내는 $S_i$와 $E_i$가 공백으로 구분되어 순서대로 주어진다. ($1\leq S_i\leq E_i\leq M$)

출력

축제 기간 중 일렬로 연속해서 핀 벚나무 개수의 최댓값과, 가장 많은 벚나무가 일렬로 연속해서 핀 날의 개수를 공백으로 구분하여 순서대로 출력한다.

예제 입력 1

3 5
3 5
1 3
1 1

예제 출력 1

2 2

예제 입력 2

5 10
8 10
6 9
1 3
5 9
1 8

예제 출력 2

2 5

예제 입력 3

3 3
1 1
2 2
3 3

예제 출력 3

1 3
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