A10374 | Mike and Geometry Problem

Mike 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 $[l_{i},r_{i}]$ 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 $1000000007$ ( $10^{9}+7$ ).

Mike can't solve this problem so he needs your help. You will help him, won't you?

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 $l_{i},r_{i}$ $(-10^{9}<=l_{i}<=r_{i}<=10^{9})$ , describing $i$ -th segment bounds.

Print one integer number — the answer to Mike's problem modulo $1000000007$ ( $10^{9}+7$ ) in the only line.