{"problem":{"name":"Line++","description":{"content":"We have an undirected graph $G$ with $N$ vertices numbered $1$ to $N$ and $N$ edges as follows: *   For each $i=1,2,...,N-1$, there is an edge between Vertex $i$ and Vertex $i+1$. *   There is an edg","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc160_d"},"statements":[{"statement_type":"Markdown","content":"We have an undirected graph $G$ with $N$ vertices numbered $1$ to $N$ and $N$ edges as follows:\n\n*   For each $i=1,2,...,N-1$, there is an edge between Vertex $i$ and Vertex $i+1$.\n*   There is an edge between Vertex $X$ and Vertex $Y$.\n\nFor each $k=1,2,...,N-1$, solve the problem below:\n\n*   Find the number of pairs of integers $(i,j) (1 \\leq i < j \\leq N)$ such that the shortest distance between Vertex $i$ and Vertex $j$ in $G$ is $k$.\n\n## Constraints\n\n*   $3 \\leq N \\leq 2 \\times 10^3$\n*   $1 \\leq X,Y \\leq N$\n*   $X+1 < Y$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $X$ $Y$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc160_d","tags":[],"sample_group":[["5 2 4","5\n4\n1\n0\n\nThe graph in this input is as follows:  \n  \n![image](https://img.atcoder.jp/ghi/3ae0885a4aeda99694b9fde4efe39dc1.png)  \n  \nThere are five pairs $(i,j) (1 \\leq i < j \\leq N)$ such that the shortest distance between Vertex $i$ and Vertex $j$ is $1$: $(1,2)\\,,(2,3)\\,,(2,4)\\,,(3,4)\\,,(4,5)$.  \nThere are four pairs $(i,j) (1 \\leq i < j \\leq N)$ such that the shortest distance between Vertex $i$ and Vertex $j$ is $2$: $(1,3)\\,,(1,4)\\,,(2,5)\\,,(3,5)$.  \nThere is one pair $(i,j) (1 \\leq i < j \\leq N)$ such that the shortest distance between Vertex $i$ and Vertex $j$ is $3$: $(1,5)$.  \nThere are no pairs $(i,j) (1 \\leq i < j \\leq N)$ such that the shortest distance between Vertex $i$ and Vertex $j$ is $4$."],["3 1 3","3\n0\n\nThe graph in this input is as follows:  \n  \n![image](https://img.atcoder.jp/ghi/be2921b3b307fc993a390a59437e624e.png)"],["7 3 7","7\n8\n4\n2\n0\n0"],["10 4 8","10\n12\n10\n8\n4\n1\n0\n0\n0"]],"created_at":"2026-03-03 11:01:14"}}