{"raw_statement":[{"iden":"problem statement","content":"The Republic of AtCoder has $N$ cities, called City $1$, City $2$, $\\ldots$, City $N$. Initially, there was a bidirectional road between every pair of different cities, but $M$ of these roads have become unusable due to deterioration over time. More specifically, for each $1\\leq i \\leq M$, the road connecting City $U_i$ and City $V_i$ has become unusable.\nTakahashi will go for a $K$\\-day trip that starts and ends in City $1$. Formally speaking, a $K$\\-day trip that starts and ends in City $1$ is a sequence of $K+1$ cities $(A_0, A_1, \\ldots, A_K)$ such that $A_0=A_K=1$ holds and for each $0\\leq i\\leq K-1$, $A_i$ and $A_{i+1}$ are different and there is still a usable road connecting City $A_i$ and City $A_{i+1}$.\nPrint the number of different $K$\\-day trips that start and end in City $1$, modulo $998244353$. Here, two $K$\\-day trips $(A_0, A_1, \\ldots, A_K)$ and $(B_0, B_1, \\ldots, B_K)$ are said to be different when there exists an $i$ such that $A_i\\neq B_i$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 5000$\n*   $0 \\leq M \\leq \\min\\left( \\frac{N(N-1)}{2},5000 \\right)$\n*   $2 \\leq K \\leq 5000$\n*   $1 \\leq U_i<V_i \\leq N$\n*   All pairs $(U_i, V_i)$ are pairwise distinct.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n$U_1$ $V_1$\n$:$\n$U_M$ $V_M$"},{"iden":"sample input 1","content":"3 1 4\n2 3"},{"iden":"sample output 1","content":"4\n\nThere are four different trips as follows.\n\n*   ($1,2,1,2,1$)\n*   ($1,2,1,3,1$)\n*   ($1,3,1,2,1$)\n*   ($1,3,1,3,1$)\n\nNo other trip is valid, so we should print $4$."},{"iden":"sample input 2","content":"3 3 3\n1 2\n1 3\n2 3"},{"iden":"sample output 2","content":"0\n\nNo road remains usable, so there is no valid trip."},{"iden":"sample input 3","content":"5 3 100\n1 2\n4 5\n2 3"},{"iden":"sample output 3","content":"428417047"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}