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:
class Tree(): #weighted
    def __init__(self, n, edge):
        self.n = n
        self.tree = [[] for _ in range(n)]
        for e in edge:
            self.tree[e[0] - 1].append((e[1] - 1, e[2] - 1, e[3]))
            self.tree[e[1] - 1].append((e[0] - 1, e[2] - 1, e[3]))

    def setroot(self, root):
        self.root = root
        self.parent = [None for _ in range(self.n)]
        self.parent[root] = -1
        self.depth = [None for _ in range(self.n)]
        self.depth[root] = 0
        self.distance = [None for _ in range(self.n)]
        self.distance[root] = 0
        self.order = []
        self.order.append(root)
        self.color = [None for _ in range(self.n)]
        self.cost = [0 for _ in range(self.n)]
        self.size = [1 for _ in range(self.n)]
        stack = [root]
        while stack:
            node = stack.pop()
            for adj, color, cost in self.tree[node]:
                if self.parent[adj] is None:
                    self.parent[adj] = node
                    self.depth[adj] = self.depth[node] + 1
                    self.distance[adj] = self.distance[node] + cost
                    self.color[adj] = color
                    self.cost[adj] = cost
                    self.order.append(adj)
                    stack.append(adj)
        for node in self.order[::-1]:
            for adj, color, cost in self.tree[node]:
                if self.parent[node] == adj:
                    continue
                self.size[node] += self.size[adj]

    def heavylight_decomposition(self):
        self.order = [None for _ in range(self.n)]
        self.head = [None for _ in range(self.n)]
        self.head[self.root] = self.root
        self.next = [None for _ in range(self.n)]
        stack = [self.root]
        order = 0
        while stack:
            node = stack.pop()
            self.order[node] = order
            order += 1
            maxsize = 0
            for adj, color, cost in self.tree[node]:
                if self.parent[node] == adj:
                    continue
                if maxsize < self.size[adj]:
                    maxsize = self.size[adj]
                    self.next[node] = adj
            for adj, color, cost in self.tree[node]:
                if self.parent[node] == adj or self.next[node] == adj:
                    continue
                self.head[adj] = adj
                stack.append(adj)
            if self.next[node] is not None:
                self.head[self.next[node]] = self.head[node]
                stack.append(self.next[node])

    def range_hld(self, u, v, edge=False):
        res = []
        while True:
            if self.order[u] > self.order[v]: u, v = v, u
            if self.head[u] != self.head[v]:
                res.append((self.order[self.head[v]], self.order[v] + 1))
                v = self.parent[self.head[v]]
            else:
                res.append((self.order[u] + edge, self.order[v] + 1))
                return res

    def subtree_hld(self, u):
        return self.order[u], self.order[u] + self.size[u]

    def lca_hld(self, u, v):
        while True:
            if self.order[u] > self.order[v]: u, v = v, u
            if self.head[u] != self.head[v]:
                v = self.parent[self.head[v]]
            else:
                return u

class SegmentTree():
    def __init__(self, arr, func=min, ie=2**63):
        self.h = (len(arr) - 1).bit_length()
        self.n = 2**self.h
        self.ie = ie
        self.func = func
        self.tree = [ie for _ in range(2 * self.n)]
        for i in range(len(arr)):
            self.tree[self.n + i] = arr[i]
        for i in range(1, self.n)[::-1]:
            self.tree[i] = func(self.tree[2 * i], self.tree[2 * i + 1])

    def set(self, idx, x):
        idx += self.n
        self.tree[idx] = x
        while idx:
            idx >>= 1
            self.tree[idx] = self.func(self.tree[2 * idx], self.tree[2 * idx + 1])

    def query(self, lt, rt):
        lt += self.n
        rt += self.n
        vl = vr = self.ie
        while rt - lt > 0:
            if lt & 1:
                vl = self.func(vl, self.tree[lt])
                lt += 1
            if rt & 1:
                rt -= 1
                vr = self.func(self.tree[rt], vr)
            lt >>= 1
            rt >>= 1
        return self.func(vl, vr)

import sys
input = sys.stdin.readline

N, Q = map(int, input().split())

edge = [tuple(map(int, input().split())) for _ in range(N - 1)]
query = [tuple(map(int, input().split())) for _ in range(Q)]

tree = Tree(N, edge)
tree.setroot(0)
tree.heavylight_decomposition()

arr = [None for _ in range(N)]

for i in range(N):
    arr[tree.order[i]] = (tree.cost[i], 0)

def func(x, y):
    x0, x1 = x
    y0, y1 = y
    return x0 + y0, x1 + y1

ie = (0, 0)

st = SegmentTree(arr, func, ie)

query_color = [[] for _ in range(N)]

for j in range(Q):
    x, y, u, v = query[j]
    query_color[x - 1].append((y, u, v, j))

node_color = [[] for _ in range(N)]

for i in range(1, N):
    node_color[tree.color[i]].append(i)

res = [0 for _ in range(Q)]

for i in range(N):
    for node in node_color[i]:
        st.set(tree.order[node], (0, 1))

    for y, u, v, j in query_color[i]:
        for lt, rt in tree.range_hld(u - 1, v - 1, True):
            d, k = st.query(lt, rt)
            res[j] += d + k * y

    for node in node_color[i]:
        st.set(tree.order[node], (tree.cost[node], 0))

print('\n'.join(map(str, res)))