CF623E.Transforming Sequence
普及/提高-
通过率:0%
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题目描述
Let's define the transformation P of a sequence of integers a1,a2,...,an as b1,b2,...,bn , where bi=a1 ∣ a2 ∣ ... ∣ ai for all i=1,2,...,n , where ∣ is the bitwise OR operation.
Vasya consequently applies the transformation P to all sequences of length n consisting of integers from 1 to 2k−1 inclusive. He wants to know how many of these sequences have such property that their transformation is a strictly increasing sequence. Help him to calculate this number modulo 109+7 .
输入格式
The only line of the input contains two integers n and k ( 1<=n<=1018,1<=k<=30000 ).
输出格式
Print a single integer — the answer to the problem modulo 109+7 .
输入输出样例
输入#1
1 2
输出#1
3
输入#2
2 3
输出#2
30
输入#3
3 3
输出#3
48