{"raw_statement":[{"iden":"problem statement","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 $k$."},{"iden":"constraints","content":"*   $3 \\leq N \\leq 2 \\times 10^3$\n*   $1 \\leq X,Y \\leq N$\n*   $X+1 < Y$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $X$ $Y$"},{"iden":"sample input 1","content":"5 2 4"},{"iden":"sample output 1","content":"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 $4$."},{"iden":"sample input 2","content":"3 1 3"},{"iden":"sample output 2","content":"3\n0\n\nThe graph in this input is as follows:  \n  \n![image](https://img.atcoder.jp/ghi/be2921b3b307fc993a390a59437e624e.png)"},{"iden":"sample input 3","content":"7 3 7"},{"iden":"sample output 3","content":"7\n8\n4\n2\n0\n0"},{"iden":"sample input 4","content":"10 4 8"},{"iden":"sample output 4","content":"10\n12\n10\n8\n4\n1\n0\n0\n0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}