PERMUT1 - Permutations

题意翻译

在一个有n个元素(1~n)的序列中,**查找这个序列的全排列中一共有多少个排列含有k个逆序对。** 比如当n=4,k=1时,一共有3个排列含有1个逆序对 (友情提示:1243、1324、2134) ### 输入格式: 第一行输入一个d(1<=d<=10),表示一共有d组数据。 对于每组数据,会输入整数n(1<=n<=12) 和整数k(0<=k<=98) ### 输出格式 每行输出每组数据的答案。

题目描述

Let A = \[a $ _{1} $ ,a $ _{2} $ ,...,a $ _{n} $ \] be a permutation of integers 1,2,...,n. A pair of indices (i,j), 1<=i<=j<=n, is an _inversion_ of the permutation A if a $ _{i} $ >a $ _{j} $ . We are given integers n>0 and k>=0. What is the number of n-element permutations containing exactly k inversions? For instance, the number of 4-element permutations with exactly 1 inversion equals 3. ### Task Write a program which for each data set from a sequence of several data sets: - reads integers n and k from input, - computes the number of n-element permutations with exactly k inversions, - writes the result to output.

输入输出格式

输入格式


The first line of the input file contains one integer d, 1<=d<=10, which is the number of data sets. The data sets follow. Each data set occupies one line of the input file and contains two integers n (1<=n<=12) and k (0<=k<=98) separated by a single space.

输出格式


The i-th line of the output file should contain one integer - the number of n-element permutations with exactly k inversions.

输入输出样例

输入样例 #1

1 
4 1

输出样例 #1

3