Manasva "JARVIS" Katyal is going on an adventure in his beloved Grob 120A. There are $N$ destinations connected by $N-1$ routes. The $i$th route connects destination $u_i$ with destination $v_i$, using up $l_i$ units of fuel. Routes can be flown both ways and multiple times. It is possible to reach every destination from every other destination using these routes. Since Manasva spent his life savings buying the Grob 120A, he's being really frugal and wants to save fuel. He asks $Q$ questions. For each question, he asks if it would be possible to fly from destination $1$ to $q_i$ while using exactly $c_i$ units of fuel.

Constraints

$1\le N\le {10}^3$

$1\le Q\le {10}^6$

$1\le u_i,v_i,q_i\le N$

$1\le l_i\le {10}^3$

Subtask 1 [40%]

$1\le c_i\le {10}^3$

Subtask 2 [60%]

$1\le c_i\le {10}^9$

Input Specification

The first line contains $2$ space-separated integers, $N$ and $Q$.

The next $N-1$ lines each contain $3$ space-separated integers, $u_i$, $v_i$, and $l_i$, indicating a route connecting destination $u_i$ with destination $v_i$ which uses $l_i$ units of fuel.

The next $Q$ lines each contain $2$ space-separated integers, $q_i$ and $c_i$.

Output Specification

For each query, output a single line containing YES if there exists a path and NO if there is no valid path.

Sample Input

5 4
2 1 9
1 4 4
2 5 11
3 1 6
3 24
1 17
3 21
2 47

Sample Output

YES
NO
NO
YES