Problem: There is a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and Vertex b_i, and the color and length of that edge are c_i and d_i, respectively. Here the color of each edge is represented by an integer between 1 and N-1 (inclusive). The same integer corresponds to the same color, and different integers correspond to different colors.

Answer the following Q queries:

* Query j (1 \leq j \leq Q): assuming that the length of every edge whose color is x_j is changed to y_j, find the distance between Vertex u_j and Vertex v_j. (The changes of the lengths of edges do not affect the subsequent queries.)

Constraints

* 2 \leq N \leq 10^5
* 1 \leq Q \leq 10^5
* 1 \leq a_i, b_i \leq N
* 1 \leq c_i \leq N-1
* 1 \leq d_i \leq 10^4
* 1 \leq x_j \leq N-1
* 1 \leq y_j \leq 10^4
* 1 \leq u_j < v_j \leq N
* The given graph is a tree.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N Q
a_1 b_1 c_1 d_1
:
a_{N-1} b_{N-1} c_{N-1} d_{N-1}
x_1 y_1 u_1 v_1
:
x_Q y_Q u_Q v_Q


Output

Print Q lines. The j-th line (1 \leq j \leq Q) should contain the answer to Query j.

Example

Input

5 3
1 2 1 10
1 3 2 20
2 4 4 30
5 2 1 40
1 100 1 4
1 100 1 5
3 1000 3 4


Output

130
200
60

Solution (in PYTHON3):

Solution:
import sys
from collections import defaultdict
readline = sys.stdin.readline
N, Q = map(int, readline().split())

class SegTree:
    def __init__(self, init_val, n, ide_ele, seg_func):
        self.segfunc = seg_func
        self.num = 2**(n-1).bit_length()
        self.ide_ele = ide_ele
        self.seg=[self.ide_ele]*2*self.num
        for i in range(n):
            self.seg[i+self.num-1]=init_val[i]    
        for i in range(self.num-2,-1,-1) :
            self.seg[i]=self.segfunc(self.seg[2*i+1],self.seg[2*i+2]) 
        
    def update(self, k, x):
        k += self.num-1
        self.seg[k] = x
        while k+1:
            k = (k-1)//2
            self.seg[k] = self.segfunc(self.seg[k*2+1],self.seg[k*2+2])
        
    def query(self, p, q):
        if q<=p:
            return self.ide_ele
        p += self.num-1
        q += self.num-2
        res=self.ide_ele
        while q-p>1:
            if p&1 == 0:
                res = self.segfunc(res,self.seg[p])
            if q&1 == 1:
                res = self.segfunc(res,self.seg[q])
                q -= 1
            p = p//2
            q = (q-1)//2
        if p == q:
            res = self.segfunc(res,self.seg[p])
        else:
            res = self.segfunc(self.segfunc(res,self.seg[p]),self.seg[q])
        return res

def process():

    G = [[] for _ in range(N+1)]
    dp = {}
    for v in range(N-1):
        a, b, c, d = map(int, readline().split())
        G[a].append(b)
        G[b].append(a)
        dp[(min(a,b), max(a,b))] = c, d

    S = [1]*(2*N+1)
    F = [0]*(N+1)
    stack = []
    for u in G[1]:
        stack += [-1, u]

    visited = set([1])
    depth, depthh = [0]*(N+1), [0]*(N+1)
    mmn = [[0] for _ in range(N)]
    msn = [[0] for _ in range(N)]
    iin = [[] for _ in range(N)]
    path = [1]
    ii = 0

    while True:
        if len(stack) == 0:
            break
        v = stack.pop()
        ii += 1
        if v > 0:
            visited.add(v)
            parent = path[-1]
            path.append(v)
            #print(parent)

            cc, dpd = dp[(min(v,parent), max(v,parent))]
            F[v], S[ii] = ii, v
            depth[v], depthh[v] = depth[parent] + 1, depthh[parent] + dpd

            mmn[cc].append(mmn[cc][-1]+1)
            msn[cc].append(msn[cc][-1]+dpd)
            iin[cc].append(ii)

            for u in G[v]:
                if u in visited:
                    continue
                stack += [-v, u]
        else:
            child = path.pop()
            cc, dpd = dp[(min(-v, child), max(-v, child))]
            S[ii] = v
            mmn[cc].append(mmn[cc][-1]-1)
            iin[cc].append(ii)
            msn[cc].append(msn[cc][-1]-dpd)
    # オイラーツアー
#    print(S)
#    print(depth)
#    print(F)
#    print(iin)
    stree = SegTree([(depth[abs(v)], i) for i, v in enumerate(S)], len(S), (N, None), min)

    for q in range(Q):
        x, y, u, v = map(int, readline().split())
        fu = F[u]; fv = F[v]
        if fu > fv:
            fu, fv = fv, fu

        cc = abs(S[stree.query(fu, fv+1)[1]])

        ll, mm, ms = iin[x], mmn[x], msn[x]
        uvcs = []
        for target_i in [F[u], F[v], F[cc]]:
            if not ll:
                uvcs.append((0,0))
                continue
            ind, lw, hw =  (len(ll)-1)//2, 0, len(ll)-1
            if target_i < ll[0] or target_i >= ll[-1]:
                uvcs.append((0,0))
                continue
            while True:
                if ll[ind] <= target_i:
                    if target_i < ll[ind+1]:
                        uvcs.append((mm[ind+1], ms[ind+1]))
                        break
                    ind, lw = (ind+1 + hw)//2, ind+1
                    continue
                ind, hw = (ind-1 + lw)//2, ind-1
        diff = (uvcs[0][0] + uvcs[1][0] - 2 * uvcs[2][0]) * y - (uvcs[0][1] + uvcs[1][1] - 2 * uvcs[2][1])
        print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)


if __name__ == '__main__':
    process()