ZBRKA - Problème

#17566. ZBRKA

Statistiques

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考虑一个长度为 $N$ 的整数序列，其中 $1$ 到 $N$ 之间的每个整数恰好出现一次。

如果序列中较早出现的数字大于较晚出现的数字，则称这一对数是混乱的。

序列的混乱度是其中混乱对的数量。例如，序列 $(1, 4, 3, 2)$ 的混乱度为 $3$，因为其中有 $3$ 个混乱对：$(4, 3)$、$(4, 2)$ 和 $(3, 2)$。

编写一个程序，计算长度为 $N$ 且混乱度恰好为 $C$ 的序列数量。

输入格式

输入只有一行，包含两个整数 $N$（$1 \le N \le 1000$）和 $C$（$0 \le C \le 10000$）。

输出格式

输出符合条件的序列数量模 $1000000007$ 的结果。

样例

输入样例 1

10 1

输出样例 1

输入样例 2

4 3

输出样例 2

输入样例 3

9 13

输出样例 3

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