시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB144615550.459%

문제

총 N개의 역을 지나가는 기차가 있다. (첫 역과 마지막 역도 포함한다)

기차가 첫 역을 출발할 때와 마지막 역에 도착할 때, 탑승하고 있는 승객은 아무도 없다. 각 역에서 기차를 타는 승객의 수와 기차에서 내리는 승객의 수는 입력으로 주어진다.

각 승객은 기차를 타고 역 몇 개를 지난 뒤에 지하철에서 내리고, 같은 열차를 두 번 이상 타지 않는다.

이 기차에는 기차표를 검사하는 직원이 타고 있다. 이 직원은 기차가 첫 번째 역에서 두 번째 역으로 가는 동안 기차를 타고 있는 모든 승객의 기차표를 검사한다. 그 다음에는 기차가 역 K개를 지날 때마다 표를 검사한다. (일반화 하면 a*K+1 번째 역에서 a*K+2 번째 역으로 가는 동안 검사한다) 따라서, 기차를 타고 있는 동안 기차표를 한 번도 검사받지 않는 승객이 있을 수도 있다.

이때, 기차표를 한 번도 검사받지 않는 승객 수의 최솟값과 최댓값을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 N과 K가 주어진다. (2 ≤ N ≤ 1000, 1 ≤ K ≤ 1000)

다음 N개 줄에는 각 역에서 기차에서 내리는 승객의 수와 기차를 타는 승객의 수가 공백으로 구분되어져서 주어진다. (기차가 지나가는 역을 순서대로 주어진다) 모든 숫자는 0보다 크거나 같고, 1000보다 크지 않다.

출력

첫째 줄에 기차표를 한 번도 검사받지 않는 승객 수의 최솟값과 최댓값을 공백으로 구분해서 출력한다.

예제 입력 1

3 2
0 5
4 2
3 0

예제 출력 1

2 2

예제 입력 2

4 2
0 5
0 5
3 0
7 0

예제 출력 2

0 3

예제 입력 3

6 2
0 10
5 3
6 4
2 8
8 1
5 0

예제 출력 3

5 11
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