8357번 - Cliquers Strike Back 다국어

문제

An undirected graph is called a labeled cliquer if each connected component of the graph is a clique and the vertices of the graph are numbered with numbers from the set {1, ..., n}. Maurycy has drawn all labeled cliquers with n vertices on a piece of paper and is going to assess beauty of each of them with a number from the set {1, ..., m} (in particular, different cliquers may be assigned equal grades). In how many ways can he do this? The result should be computed modulo 10⁹ - 401. The figure below depicts all labeled cliquers for n = 3.

입력

The only line of the standard input contains two integers n and m (1 ≤ n, m ≤ 10¹⁸), separated by a single space and denoting the number of vertices of each labeled cliquer and the number of grades respectively.

출력

The only line of the standard output should contain the number of possible sets of grades modulo 10⁹ - 401.

제한

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