{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 3000$\n*   $0 \\leq X \\leq M \\le 3000$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N \\ M \\ X$"},{"iden":"sample input 1","content":"3 1 1"},{"iden":"sample output 1","content":"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*   $A=(0,0,1), \\ B=(0,0,1)$"},{"iden":"sample input 2","content":"3 1 0"},{"iden":"sample output 2","content":"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*   $A=(0,0,1), \\ B=(0,1,0)$"},{"iden":"sample input 3","content":"4 4 2"},{"iden":"sample output 3","content":"643\n\nThe followings are examples of possible pairs.\n\n*   $A=(1,1,1,1), \\ B=(1,1,1,1)$\n*   $A=(1,0,0,3), \\ B=(0,1,0,3)$"},{"iden":"sample input 4","content":"314 1592 653"},{"iden":"sample output 4","content":"755768689"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}