G :: Binary Stirling Numbers

Time Limit: 2 Seconds Memory Limit: 65536 KB

The Stirling number of the second kind S(n, m) stands for the number of ways to partition a set of n things into m nonempty subsets. For example, there are seven ways to split a four-element set into two parts:

{1, 2, 3} U {4}, {1, 2, 4} U {3}, {1, 3, 4} U {2}, {2, 3, 4} U {1}
{1, 2} U {3, 4}, {1, 3} U {2, 4}, {1, 4} U {2, 3}.

Your task is much "easier". Given integers n and m satisfying 1 <= m <= n, compute the parity of S(n, m), i.e. S(n, m) mod 2.

Write a program which for each data set:

reads two positive integers n and m,

computes S(n, m) mod 2,

writes the result.

Input

The first line of the input contains exactly one positive integer d equal to the number of data sets, 1 <= d <= 200. The data sets follow.

Line i + 1 contains the i-th data set - exactly two integers ni and mi separated by a single space, 1 <= mi <= ni <= 10^9.

Output

The output should consist of exactly d lines, one line for each data set. Line i, 1 <= i <= d, should contain 0 or 1, the value of S(n_i, m_i) mod 2.

Sample Input

1
4 2

Sample Output

Submit