#1118Binary Stirling Numbers

The Stirling number of the second kind S(n, m) represents 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} ∪ {4}, {1, 2, 4} ∪ {3}, {1, 3, 4} ∪ {2}, {2, 3, 4} ∪ {1}, {1, 2} ∪ {3, 4}, {1, 3} ∪ {2, 4}, {1, 4} ∪ {2, 3}.

We can compute S(n, m) using the recurrence,

but your task is slightly different: given integers n and m, compute the parity of S(n, m), i.e. S(n, m) mod 2.

Example: S(4, 2) mod 2 = 1.

Write a program that reads two positive integers n and m, computes S(n, m) mod 2, and writes the result.

Input

The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also a blank line between two consecutive inputs.

The input consists two integers n and m separated by a space, with 1 ≤ m ≤ n ≤ 1000000000.

Output

For each test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line.

The output should be the integer S(n, m) mod 2.