BINSTIRL - Binary Stirling Numbers

给定$n,m$，求$S(n,m)\%2$ $S$为第二类斯特林数

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 you 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. For instance, S(4, 2) mod 2 = 1. ### Task Write a program that: - reads two positive integers n and m, - computes S(n, m) mod 2, - writes the result.

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 n $ _{i} $ and m $ _{i} $ separated by a single space, 1 < = m $ _{i} $ < = n $ _{i} $ <= 10 $ ^{9} $ .

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.

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