BINSTIRL - Binary Stirling Numbers

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.

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 <= 109.

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.

Example

Sample input:
1
4 2

Sample output:
1

Added by:adrian
Date:2004-07-02
Time limit:3s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:ACM Central European Programming Contest, Warsaw 2001

hide comments
2020-05-10 21:31:24
AC ... O(1) :)
2017-03-03 14:06:11
OK, challenge accepted and completed: AC with O(1), without help from teh internets. For me, visual representation was key.

Last edit: 2017-03-03 14:07:12
2016-08-24 04:56:14
How to derive the formula of the parity of the stirling numbers of the second kind that works in O(1) time ?
2016-04-26 15:07:54 gautam
O(1)...;-)
2015-08-15 14:49:57 Vishesh Middha
providing SIGSEGV error why please explain??
2015-07-28 05:54:23 (Tjandra Satria Gunawan)(曾毅昆)
Solve this problem without taking help from net? Challenge accepted ;-)
2014-12-28 23:04:26 Rajat (1307086)
Challenge for those who do not know Binary Stirling numbers:
"Do this question without taking help from net."
2014-12-20 09:51:15 sunil gowda
how to do in O(1) time .. anyone knows..
2014-10-02 17:12:20 parijat bhatt
@ j1k7_7(JaskamalKainth)
how can it be solved in o(1)
2014-08-13 17:02:56 Anubhav Balodhi
Sierpinski Gasket does it all ^_^
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