Define f(n) as the number of ways to perform n in format of the sum of some positive integers. For instance, when n=4, we have
4=1+1+1+1
4=1+1+2
4=1+2+1
4=2+1+1
4=1+3
4=2+2
4=3+1
4=4
totally 8 ways. Actually, we will have f(n)=2
(n-1) after observations.
Given a pair of integers n and k, your task is to figure out how many times that the integer k occurs in such 2
(n-1) ways. In the example above, number 1 occurs for 12 times, while number 4 only occurs once.
The first line contains a single integer T(1≤T≤10000), indicating the number of test cases.
Each test case contains two integers n and k(1≤n,k≤10
9).
Output the required answer modulo 10
9+7 for each test case, one per line.