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}.

There is a recurrence which allows to compute S(n, m) for all m and n.

S(0, 0) = 1; S(n, 0) = 0 for n > 0; S(0, m) = 0 for m > 0;

S(n, m) = m S(n - 1, m) + S(n - 1, m - 1), for n, m > 0.

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.

**Example**

S(4, 2) mod 2 = 1.

**Task**

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(ni, mi) mod 2.

**Sample Input**

1

4 2

**Sample Output**

1

Source:

**Central Europe 2001**
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