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4 초 | 256 MB | 11 | 1 | 1 | 10.000% |
A small island country is developing its transport network. Some of the islands are connected by bridges in such way that there is a unique path between any two islands. In other words, bridges form a tree. Bridges can have different length.
Before opening these bridges to the public it is required to test their safety. To do that, two testers will be traversing some paths with a speed 1 every day for the next q days. Each one will go along his own path, possibly starting at different time. Let's call a bridge tested on i-th day if both testers were going along that bridge during some non-zero time interval. For each of q days determine, if there was a bridge that was tested during that day.
The first line contains two integers n and q (1 ≤ n, q ≤ 105, n ≥ 2) — the number of islands and testing days. The following n - 1 lines describe bridges as follows: ui vi li (1 ≤ ui, vi ≤ n, 1 ≤ li ≤ 109) — endpoints of i-th bridge and its length. The following q lines contain description of the two paths. Each path is described by three numbers bi, ei, si (1 ≤ bi, ei ≤ n, 1 ≤ si ≤ 109, bi ≠ ei) — starting island, ending island and starting time for that tester.
Output q lines with answers to queries. The i-th line should contains «YES», if at least one bridge was tested during the i-th day, and «NO» otherwise.
8 6 1 2 3 1 3 1 1 4 2 2 5 5 2 6 1 5 7 2 5 8 4 5 3 2 7 4 2 8 6 1 1 7 6 4 5 1 4 5 10 7 8 3 3 4 5 6 7 6 5 1 2 2 1 10 8 3 3
YES YES NO NO NO YES