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#F1269. Different Subsets For All Tuples

    ID: 1275 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 8 上传者: 标签>组合数学数学挑战难度共享题库Codeforces英文题面题目来源题面语言

Different Subsets For All Tuples

题目描述

E. Different Subsets For All Tuples
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

For a sequence a of n integers between 1 and m, inclusive, denote f(a) as the number of distinct subsequences of a (including the empty subsequence).

You are given two positive integers n and m. Let S be the set of all sequences of length n consisting of numbers from 1 to m. Compute the sum f(a) over all a in S modulo 109+7.

Input

The only line contains two integers n and m (1≤n,m≤106) − the number of elements in arrays and the upper bound for elements.

Output

Print the only integer c − the desired sum modulo 109+7.

Examples
Input
1 3
Output
6
Input
2 2
Output
14
Input
3 3
Output
174

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 754 题。保留原作者与原赛事署名。