401936: GYM100589 D Desolation of Smaug

Frodo Baggins is trying to run from the fury of Smaug. Let’s assume we represent our city by a weighted undirected connected graph(with no self-loops and multi-edges) with N nodes and N edges.

You will be given Q queries of form S_t, D_e, S, V_f, V_S which denotes:

Frodo is currently at node S_t and needs to reach node D_e. He moves with constant velocity V_f. Smaug is currently at node S and he moves with constant velocity V_S. Print "YES"(quotes for clarity), if Frodo can reach destination without being caught by Smaug no matter what path Smaug takes. Else print "NO"(quotes for clarity).

Note: If Frodo reaches at destination at same time as Smaug, print "NO".

First line contains N and Q, the number of nodes and number of queries respectively. Each of the next N lines contain integers u, v and w denoting an undirected edge between nodes numbered u and v, w being the weight of the edge.

Each of the next Q lines contain queries.

For each query print the required answer in one line.

Constraints

• 1 ≤ N, Q ≤ 10⁵
• 1 ≤ u, v, S_t, D_e, S ≤ N
• 1 ≤ V_F, V_S, w ≤ 1000

5 2
1 2 2
2 3 3
3 4 7
4 5 5
5 1 6
1 3 5 1 2
2 4 5 2 2

YES
NO