import sys input = lambda : sys.stdin.readline().rstrip() sys.setrecursionlimit(2*10**5+10) write = lambda x: sys.stdout.write(x+"\n") debug = lambda x: sys.stderr.write(x+"\n") writef = lambda x: print("{:.12f}".format(x)) class LSG: def __init__(self,n, a=None): self._n = n self._ninf = ninf x = 0 while (1 << x) < self._n: x += 1 self._log = x self._size = 1 << self._log self._d = [ninf] * (2 * self._size) self._lz = [f0] * self._size if a is not None: for i in range(self._n): self._d[self._size + i] = a[i] for i in range(self._size - 1, 0, -1): self._update(i) def check(self): return [self.query_point(p) for p in range(self._n)] def update_point(self, p, x): p += self._size for i in range(self._log, 0, -1): self._push(p >> i) self._d[p] = x for i in range(1, self._log + 1): self._update(p >> i) def query_point(self, p): p += self._size for i in range(self._log, 0, -1): self._push(p >> i) return self._d[p] def query(self, left, right): if left == right: return ninf left += self._size right += self._size for i in range(self._log, 0, -1): if ((left >> i) << i) != left: self._push(left >> i) if ((right >> i) << i) != right: self._push(right >> i) sml = ninf smr = ninf while left < right: if left & 1: sml = op(sml, self._d[left]) left += 1 if right & 1: right -= 1 smr = op(self._d[right], smr) left >>= 1 right >>= 1 return op(sml, smr) def query_all(self): return self._d[1] def update(self, left, right, f): if right is None: p = left p += self._size for i in range(self._log, 0, -1): self._push(p >> i) self._d[p] = mapping(f, self._d[p]) for i in range(1, self._log + 1): self._update(p >> i) else: if left == right: return left += self._size right += self._size for i in range(self._log, 0, -1): if ((left >> i) << i) != left: self._push(left >> i) if ((right >> i) << i) != right: self._push((right - 1) >> i) l2 = left r2 = right while left < right: if left & 1: self._all_apply(left, f) left += 1 if right & 1: right -= 1 self._all_apply(right, f) left >>= 1 right >>= 1 left = l2 right = r2 for i in range(1, self._log + 1): if ((left >> i) << i) != left: self._update(left >> i) if ((right >> i) << i) != right: self._update((right - 1) >> i) def _update(self, k): self._d[k] = op(self._d[2 * k], self._d[2 * k + 1]) def _all_apply(self, k, f) -> None: self._d[k] = mapping(f, self._d[k]) if k < self._size: self._lz[k] = composition(f, self._lz[k]) def _push(self, k): self._all_apply(2 * k, self._lz[k]) self._all_apply(2 * k + 1, self._lz[k]) self._lz[k] = f0 def loc(self, l, r): return self._lz[self._size+l : self._size+r] from itertools import chain class HLD: def __init__(self, g, root=0, a=None): """g: 隣接行列 root : 木の根 a: 遅延セグ木に与える配列 """ self.g = g self.n = len(g) self.parent = [-1]*self.n self.size = [1]*self.n self.head = [0]*self.n self.preorder = [0]*self.n self.k = 0 self.depth = [0]*self.n for v in chain(range(root, self.n), range(0, root)): if self.parent[v] == -1: self.dfs_pre(v) self.dfs_hld(v) if a is not None: na = [0]*self.n for i in range(self.n): na[self.preorder[i]] = a[i] self.sg = LSG(self.n, na) def dfs_pre(self, v): g = self.g stack = [v] order = [v] while stack: v = stack.pop() for u in g[v]: if self.parent[v] == u: continue self.parent[u] = v self.depth[u] = self.depth[v]+1 stack.append(u) order.append(u) # 隣接リストの左端: heavyな頂点への辺 # 隣接リストの右端: 親への辺 while order: v = order.pop() child_v = g[v] if len(child_v) and child_v[0] == self.parent[v]: child_v[0], child_v[-1] = child_v[-1], child_v[0] for i, u in enumerate(child_v): if u == self.parent[v]: continue self.size[v] += self.size[u] if self.size[u] > self.size[child_v[0]]: child_v[i], child_v[0] = child_v[0], child_v[i] def dfs_hld(self, v): stack = [v] while stack: v = stack.pop() self.preorder[v] = self.k self.k += 1 top = self.g[v][0] # 隣接リストを逆順に見ていく(親 > lightな頂点への辺 > heavyな頂点 (top)) # 連結成分が連続するようにならべる for u in reversed(self.g[v]): if u == self.parent[v]: continue if u == top: self.head[u] = self.head[v] else: self.head[u] = u stack.append(u) def for_each(self, u, v): # [u, v]上の頂点集合の区間を列挙 while True: if self.preorder[u] > self.preorder[v]: u, v = v, u l = max(self.preorder[self.head[v]], self.preorder[u]) r = self.preorder[v] yield l, r # [l, r] if self.head[u] != self.head[v]: v = self.parent[self.head[v]] else: return def for_each_edge(self, u, v): # [u, v]上の辺集合の区間列挙 # 辺の情報は子の頂点に while True: if self.preorder[u] > self.preorder[v]: u, v = v, u if self.head[u] != self.head[v]: yield self.preorder[self.head[v]], self.preorder[v] v = self.parent[self.head[v]] else: if u != v: yield self.preorder[u]+1, self.preorder[v] break def subtree(self, v): # 頂点vの部分木の頂点集合の区間 [l, r) l = self.preorder[v] r = self.preorder[v]+self.size[v] return l, r def lca(self, u, v): # 頂点u, vのLCA while True: if self.preorder[u] > self.preorder[v]: u, v = v, u if self.head[u] == self.head[v]: return u v = self.parent[self.head[v]] def update(self, u, v, val): for l,r in self.for_each(u,v): self.sg.update(l,r+1,val) def query(self, u, v): res = ninf for l,r in self.for_each(u,v): res = op(res, self.sg.query(l,r+1)) return res def update_edge(self, u, v, val): for l,r in self.for_each_edge(u,v): self.sg.update(l,r+1,val) def query_edge(self, u, v): res = ninf for l,r in self.for_each_edge(u,v): res = op(res, self.sg.query(l,r+1)) return res def t2i(*vs): n = len(vs)+1 nvs = [1] val = 1 for v in vs[::-1]: val *= v nvs.append(val) vs = nvs[::-1] tos = "def to(%s):\n" % (",".join([f"v{i}" for i in range(n)])) tos += " val = 0\n" for i,v in enumerate(vs): tos += f" val += {v} * v{i}\n" tos += " return val" frms = f"def frm(val):\n" for i in range(n-1): frms += f" v{i},val = divmod(val, {vs[i]})\n" frms += " return %s" % ((", ".join([f"v{i}" for i in range(n-1)]) + ", val")) return tos, frms tos, frms = t2i(1<<30) exec(tos) exec(frms) # 区間和・区間加算の例 M = 10**9+7 ninf = to(0,0) f0 = 0 def op(x,y): x = frm(x) y = frm(y) xx = x[0]+y[0] yy = x[1]+y[1] return to(xx%M,yy%M) def mapping(f,x): x = frm(x) return to((f*x[1] + x[0])%M, x[1]) # composition: あとからきたクエリがf1に入る def composition(f1,f2): return (f1+f2)%M n = int(input()) s = list(map(int, input().split())) c = list(map(int, input().split())) ns = [[] for _ in range(n)] for _ in range(n-1): u,v = map(int, input().split()) u -= 1 v -= 1 ns[u].append(v) ns[v].append(u) hld = HLD(ns, a=[to(ss,cc) for ss,cc in zip(s,c)]) q = int(input()) ans = [] for i in range(q): t = list(map(int, input().split())) if t[0]==0: _,x,y,z = t x -= 1 y -= 1 hld.update(x,y,z) else: _,x,y = t x -= 1 y -= 1 val = frm(hld.query(x,y)) ans.append(val[0]%M) # break write("\n".join(map(str, ans)))