{"raw_statement":[{"iden":"problem statement","content":"Given are integers $N$ and $M$. How many sequences $A$ of $N$ integers satisfy the following conditions?\n\n*   $0 \\leq A_i \\left(i = 1, 2, \\ldots, N\\right)$\n*   $\\sum_{i = 1}^{N} A_i = M$\n*   $A_1$ xor $A_2$ xor $\\cdots$ xor $A_N = 0$ (\"xor\" denotes the bitwise XOR.)\n\nSince the answer can be enormous, report it modulo $998244353$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 5000$\n*   $1 \\leq M \\leq 5000$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"5 20"},{"iden":"sample output 1","content":"475\n\nSome of the sequences $A$ satisfying the conditions follow:\n\n*   $A = \\left(10, 0, 10, 0, 0\\right)$\n*   $A = \\left(1, 2, 3, 7, 7\\right)$"},{"iden":"sample input 2","content":"10 5"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"3141 2718"},{"iden":"sample output 3","content":"371899128"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}