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 a 1, a 2, ..., a n as b 1, b 2, ..., b n, where b i = a 1 | a 2 | ... | a i 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 2 k - 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 ≤ 30 000).

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