CF623E.Transforming Sequence

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.

我们定义整数序列 $a_1, a_2, \dots, a_n$ 的变换 $P$ 为序列 $b_1, b_2, \dots, b_n$，其中对所有 $i = 1, 2, \dots, n$，有 $b_i = a_1 \mid a_2 \mid \dots \mid a_i$，其中 $\mid$ 表示按位或（bitwise OR）运算。

瓦夏依次将变换 $P$ 应用于所有长度为 $n$、且每个元素均取自 $1$ 到 $2^k - 1$（含端点）的整数序列。他想知道：在这些序列中，有多少个序列满足其变换结果是一个严格递增序列？请你帮他计算该数目对 $10^9 + 7$ 取模的结果。

The only line of the input contains two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 30 000).

输入仅包含一行，有两个整数 $n$ 和 $k$（$1 ≤ n ≤ 10^{18}$，$1 ≤ k ≤ 30\,000$）。

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

输出一个整数——该问题答案对 $10^9 + 7$ 取模的结果。