{"problem":{"name":"Coincidence","description":{"content":"You have a pair of integer sequences $A=(A_1, A_2, \\dots, A_N), B=(B_1, B_2, \\dots, B_N)$. Initially $A_i=B_i=0$ holds for all $i = 1, 2, \\dots, N$. You will perform the following operation $M$ times.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"1202Contest_d"},"statements":[{"statement_type":"Markdown","content":"You have a pair of integer sequences $A=(A_1, A_2, \\dots, A_N), B=(B_1, B_2, \\dots, B_N)$. Initially $A_i=B_i=0$ holds for all $i = 1, 2, \\dots, N$.\nYou will perform the following operation $M$ times.\n\n*   **Operation**: Choose two integers $i, j\\ (1 \\le i, j \\le N)$ and increment $A_i$ and $B_j$ by $1$.\n\nHere, out of the $M$ operations, the number of operations in which $i=j$ holds must be **exactly** $X$.\nFind the number, modulo $998244353$, of pairs of integer sequences that $A, B$ can be after the $M$ operations.\n\n## Constraints\n\n*   $2 \\leq N \\leq 3000$\n*   $0 \\leq X \\leq M \\le 3000$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N \\ M \\ X$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"1202Contest_d","tags":[],"sample_group":[["3 1 1","3\n\nThe following $3$ pairs are possible.\n\n*   $A=(1,0,0), \\ B=(1,0,0)$\n*   $A=(0,1,0), \\ B=(0,1,0)$\n*   $A=(0,0,1), \\ B=(0,0,1)$"],["3 1 0","6\n\nThe following $6$ pairs are possible.\n\n*   $A=(1,0,0), \\ B=(0,1,0)$\n*   $A=(1,0,0), \\ B=(0,0,1)$\n*   $A=(0,1,0), \\ B=(1,0,0)$\n*   $A=(0,1,0), \\ B=(0,0,1)$\n*   $A=(0,0,1), \\ B=(1,0,0)$\n*   $A=(0,0,1), \\ B=(0,1,0)$"],["4 4 2","643\n\nThe followings are examples of possible pairs.\n\n*   $A=(1,1,1,1), \\ B=(1,1,1,1)$\n*   $A=(1,0,0,3), \\ B=(0,1,0,3)$"],["314 1592 653","755768689"]],"created_at":"2026-03-03 11:01:13"}}