Sequence Sum Possibilities

Time Limit: 1000MS

Memory Limit: 65536K

Description

Most positive integers may be written as a sum of a sequence of at least two consecutive positive integers. For instance,
6 = 1 + 2 + 3
9 = 5 + 4 = 2 + 3 + 4
but 8 cannot be so written.Write a program which will compute how many different ways an input number may be written as a sum of a sequence of at least two consecutive positive integers.

Input

The first line of input will contain the number of problem instances N on a line by itself, (1 N 1000) . This will be followed by N lines, one for each problem instance. Each problem line will have the problem number, a single space and the number to be written as a sequence of consecutive positive integers. The second number will be less than 231 (so will fit in a 32-bit integer).

Output

The output for each problem instance will be a single line containing the problem number, a single space and the number of ways the input number can be written as a sequence of consecutive positive integers.

Sample Input

7
1 6
2 9
3 8
4 1800
5 987654321
6 987654323
7 987654325

Sample Output

1 1
2 2
3 0
4 8
5 17
6 1
7 23

Hint

Source

Greater New York 2005

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