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#F1387. Transforming Sequence

    ID: 1393 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 10 上传者: 标签>组合数学动态规划FFT数学挑战难度共享题库Codeforces英文题面题目来源题面语言

Transforming Sequence

题目描述

E. Transforming Sequence
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

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 890 题。保留原作者与原赛事署名。