Problem:
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The Maximum Number of Customers

$N$ persons visited a restaurant. The restaurant is open from 0 to $T$. The $i$-th person entered the restaurant at $l_i$ and left at $r_i$. Find the maximum number of persons during the business hours.

Constraints

$ 1 \leq N \leq 10^5 $

$ 1 \leq T \leq 10^5 $

$ 0 \leq l_i < r_i \leq T $

Input

The input is given in the following format.

$N$ $T$

$l_1$ $r_1$

$l_2$ $r_2$

:

$l_N$ $r_N$

Output

Print the maximum number of persons in a line.

Sample Input 1

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

Sample Output 1

4

Sample Input 2

2 2
0 1
1 2

Sample Output 2

1

Solution in C (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#define TMAX 100000
int main(void){
	int N, T, time[TMAX]={0}, in, out, max=0, full=0, i, j;
	scanf("%d%d", &N, &T);
	for(i=0; i<N; i++){
		scanf("%d%d", &in, &out);
		if(0 != in || 100000 != out){
			for(j=in; j<out; j++){
				*(time+j) += 1;
				if(max < *(time+j)){
					max = *(time+j);
				}
			}
		}else{
			full++;
		}
	}
	printf("%d\n", max+full);
	return 0;
}