4680: Mike and Geometry Problem
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：3
通过：3
题目描述
time limit per test
3 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputMike wants to prepare for IMO but he doesn't know geometry, so his teacher gave him an interesting geometry problem. Let's define f([l,r])=r-l+1 to be the number of integer points in the segment [l,r] with l≤r (say that 
). You are given two integers n and k and n closed intervals [li,ri] on OX axis and you have to find:
In other words, you should find the sum of the number of integer points in the intersection of any k of the segments.
As the answer may be very large, output it modulo 1000000007 (109+7).
Mike can't solve this problem so he needs your help. You will help him, won't you?
). You are given two integers n and k and n closed intervals [li,ri] on OX axis and you have to find: As the answer may be very large, output it modulo 1000000007 (109+7).
Mike can't solve this problem so he needs your help. You will help him, won't you?
Input
The first line contains two integers n and k (1≤k≤n≤200000)− the number of segments and the number of segments in intersection groups respectively.Then n lines follow, the i-th line contains two integers li,ri (-109≤li≤ri≤109), describing i-th segment bounds.
Output
Print one integer number− the answer to Mike's problem modulo 1000000007 (109+7) in the only line.Examples
Input
3 2
1 2
1 3
2 3
Output
5
Input
3 3
1 3
1 3
1 3
Output
3
Input
3 1
1 2
2 3
3 4
Output
6
Note
In the first example: 
;
;
.So the answer is 2+1+2=5.
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