{"raw_statement":[{"iden":"problem statement","content":"You are given positive integers $N$ and $M$. Here, it is guaranteed that $N\\leq M \\leq 2N$.\nPrint the sum, modulo $200\\ 003$ (a prime), of the following value over all sequences of positive integers $S=(S_1,S_2,\\dots,S_N)$ such that $\\displaystyle \\sum_{i=1}^{N} S_i = M$ (notice the unusual modulo):\n\n*   $\\displaystyle \\prod_{k=1}^{N} \\min(k,S_k)$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^{12}$\n*   $N \\leq M \\leq 2N$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"3 5"},{"iden":"sample output 1","content":"14\n\nThere are six sequences $S$ that satisfy the condition: $S=(1,1,3), S=(1,2,2), S=(1,3,1), S=(2,1,2), S=(2,2,1), S=(3,1,1)$.\nThe value $\\displaystyle \\prod_{k=1}^{N} \\min(k,S_k)$ for each of those $S$ is as follows.\n\n*   $S=(1,1,3)$ : $1\\times 1 \\times 3 = 3$\n*   $S=(1,2,2)$ : $1\\times 2 \\times 2 = 4$\n*   $S=(1,3,1)$ : $1\\times 2 \\times 1 = 2$\n*   $S=(2,1,2)$ : $1\\times 1 \\times 2 = 2$\n*   $S=(2,2,1)$ : $1\\times 2 \\times 1 = 2$\n*   $S=(3,1,1)$ : $1\\times 1 \\times 1 = 1$\n\nThus, you should print their sum: $14$."},{"iden":"sample input 2","content":"1126 2022"},{"iden":"sample output 2","content":"40166\n\nPrint the sum modulo $200\\ 003$."},{"iden":"sample input 3","content":"1000000000000 1500000000000"},{"iden":"sample output 3","content":"180030"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}