fireworks

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

Hmz likes to play fireworks, especially when they are put regularly.
Now he puts some fireworks in a line. This time he put a trigger on each firework. With that trigger, each firework will explode and split into two parts per second, which means if a firework is currently in position x, then in next second one part will be in position x−1 and one in x+1. They can continue spliting without limits, as Hmz likes.
Now there are n fireworks on the number axis. Hmz wants to know after T seconds, how many fireworks are there in position w?

Input

Input contains multiple test cases.
For each test case:

  • The first line contains 3 integers n,T,w(n,T,|w|≤10^5)
  • In next n lines, each line contains two integers xi and ci, indicating there are ci fireworks in position xi at the beginning(ci,|xi|≤10^5).

Output

For each test case, you should output the answer MOD 1000000007.

Sample Input

1 2 0
2 2
2 2 2
0 3
1 2

Sample Output

2
3

Hint

Source

“浪潮杯”山东省第八届ACM大学生程序设计竞赛(感谢青岛科技大学)