{"problem":{"name":"Distributing Integers","description":{"content":"We have a tree with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge in this tree connects Vertex $a_i$ and $b_i$. For each $k=1, ..., N$, solve the problem below: *   Consider writing a number on ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc160_f"},"statements":[{"statement_type":"Markdown","content":"We have a tree with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge in this tree connects Vertex $a_i$ and $b_i$. For each $k=1, ..., N$, solve the problem below:\n\n*   Consider writing a number on each vertex in the tree in the following manner:\n    *   First, write $1$ on Vertex $k$.\n    *   Then, for each of the numbers $2, ..., N$ in this order, write the number on the vertex chosen as follows:\n        *   Choose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.\n*   Find the number of ways in which we can write the numbers on the vertices, modulo $(10^9+7)$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq a_i,b_i \\leq N$\n*   The given graph is a tree.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$a_1$ $b_1$\n$:$\n$a_{N-1}$ $b_{N-1}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc160_f","tags":[],"sample_group":[["3\n1 2\n1 3","2\n1\n1\n\nThe graph in this input is as follows:\n![image](https://img.atcoder.jp/ghi/1c88b0eb716ba399b1c5d6565ab62337.png)\nFor $k=1$, there are two ways in which we can write the numbers on the vertices, as follows:\n\n*   Writing $1, 2, 3$ on Vertex $1, 2, 3$, respectively\n*   Writing $1, 3, 2$ on Vertex $1, 2, 3$, respectively"],["2\n1 2","1\n1\n\nThe graph in this input is as follows:\n![image](https://img.atcoder.jp/ghi/c47c7798f88e7bfec30fbd664dc9ad50.png)"],["5\n1 2\n2 3\n3 4\n3 5","2\n8\n12\n3\n3\n\nThe graph in this input is as follows:\n![image](https://img.atcoder.jp/ghi/e9c09403f8d96ae4e679a226993defa6.png)"],["8\n1 2\n2 3\n3 4\n3 5\n3 6\n6 7\n6 8","40\n280\n840\n120\n120\n504\n72\n72\n\nThe graph in this input is as follows:\n![image](https://img.atcoder.jp/ghi/a85459a03d436560bfe2e911d8cec4e6.png)"]],"created_at":"2026-03-03 11:01:14"}}