We consider problems concerning the number of ways in which a number can be written as a sum. If the order of the terms in the sum is taken into account the sum is called a composition and the number of compositions of n is denoted by c(n). Thus, the compositions of 3 are
3 = 3
3 = 1 + 2
3 = 2 + 1
3 = 1 + 1 + 1
So that c(3) = 4.
Suppose we denote by c(n, k) the number of compositions of n with all summands at least k. Thus, the compositions of 3 with all summands at least 2 are
3 = 3
The other three compositions of 3 all have summand 1, which is less than 2. So that c(3, 2) = 1.
Input
The first line of the input is an integer t (t <= 30), indicate the number of cases.
For each case, there is one line consisting of two integers n k (1 <= n <= 109, 1 <= k <= 30).
Output
Output c(n, k) modulo 109 + 7.
Sample Input
2
3 1
3 2
Sample Output
4
1