This problem tests your mathematic knowledge and your programming ability very much. Your task is to calculate the number of different Minimum Spanning Trees (MSTs) of a special undirected unweighted graph. The graph has n nodes numbered from 1 to n, and there is an edge between node i (1<=i<=n) and node j (1<=j<=n) if and only if 0<|i-j|<=k.

Input

Multiple test cases, the number of them(<=8) is given in the very first line.

Each test case contains one line with two space-separated numbers k(1<=k<=5) and n(1<=n<=10¹⁵).

Output

For each test case you should output one line, the number of different MSTs of the corresponding graph modulo 65521.

Example

Input:
1
3 5

Output:
75