CF622F The Sum of the k-th Powers

Description

There are well-known formulas: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF622F/5be9498766c9d969e3a6760cab8032bf2e4516ad.png), ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF622F/136a02961e04e3ae077df756f5b50353eb1651d8.png), ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF622F/ef5fbd3c33dc2a5f5200f977f6606feb4c647f7a.png). Also mathematicians found similar formulas for higher degrees. Find the value of the sum ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF622F/93e3cbcc0ffa2514081fc9f5724c4f98f477a6d1.png) modulo $ 10^{9}+7 $ (so you should find the remainder after dividing the answer by the value $ 10^{9}+7 $ ).

Input Format

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Output Format

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