{"problem":{"name":"Ex - Painting Weighted Graph","description":{"content":"Given is an undirected graph with $N$ vertices and $M$ edges. The $i$\\-th edge connects Vertices $A_i$ and $B_i$ and has a weight of $C_i$. Initially, all vertices are painted black. You can do the fo","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc235_h"},"statements":[{"statement_type":"Markdown","content":"Given is an undirected graph with $N$ vertices and $M$ edges. The $i$\\-th edge connects Vertices $A_i$ and $B_i$ and has a weight of $C_i$.\nInitially, all vertices are painted black. You can do the following operation at most $K$ times.\n\n*   Operation: choose any vertex $v$ and any integer $x$. Paint red all vertices reachable from the vertex $v$ by traversing edges whose weights are at most $x$, including $v$ itself.\n\nHow many sets can be the set of vertices painted red after the operations?  \nFind the count modulo $998244353$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 10^5$\n*   $0 \\leq M \\leq 10^5$\n*   $1 \\leq K \\leq 500$\n*   $1 \\leq A_i,B_i \\leq N$\n*   $1 \\leq C_i \\leq 10^9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n$A_1$ $B_1$ $C_1$\n$\\vdots$\n$A_M$ $B_M$ $C_M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc235_h","tags":[],"sample_group":[["3 2 1\n1 2 1\n2 3 2","6\n\nFor example, an operation with $(v,x)=(2,1)$ paints Vertices $1,2$ red, and an operation with $(v,x)=(1,0)$ paints Vertex $1$.\nAfter at most one operation, the set of vertices painted red can be one of the following six: ${},{1},{2},{3},{1,2},{1,2,3}$."],["5 0 2","16\n\nThe given graph may not be connected."],["6 8 2\n1 2 1\n2 3 2\n3 4 3\n4 5 1\n5 6 2\n6 1 3\n1 2 10\n1 1 100","40\n\nThe given graph may have multi-edges and self-loops."]],"created_at":"2026-03-03 11:01:14"}}