Problem2106--Transforming Sequence

2106: Transforming Sequence

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
7 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

The only line of the input contains two integers n and k (1≤n≤1018,1≤k≤30000).

Output

Print a single integer− the answer to the problem modulo 109+7.

Examples
Input
1 2
Output
3
Input
2 3
Output
30
Input
3 3
Output
48

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