using System; using System.Linq; using System.Linq.Expressions; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Point = System.Numerics.Complex; using Number = System.Int32; namespace Program { public class Solver { public void Solve() { var n = sc.Integer(); var G = new HLTreeGraph(n); G.A = sc.Integer(n); G.B = sc.Integer(n); for (int i = 0; i < n - 1; i++) { var a = sc.Integer() - 1; var b = sc.Integer() - 1; G.AddEdge(a, b); } G.Build(0); var q = sc.Integer(); for (int i = 0; i < q; i++) { if (sc.Integer() == 0) { var x = sc.Integer() - 1; var y = sc.Integer() - 1; var z = sc.Integer(); var lca = G.GetLCA(x, y); G.Update(lca, x, z); G.Update(lca, y, z); G.Update(lca, lca, -z); } else { var x = sc.Integer() - 1; var y = sc.Integer() - 1; var lca = G.GetLCA(x, y); ModInteger ans = 0; ans += G.Query(lca, x); ans += G.Query(lca, y); ans -= G.Query(lca, lca); IO.Printer.Out.WriteLine(ans); } } } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer: StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b)); if (b == 0) return long.MinValue; if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } #endregion #region ModNumber public partial struct ModInteger { public const long Mod = (long)1e9 + 7; public long num; public ModInteger(long n) : this() { num = n % Mod; if (num < 0) num += Mod; } public override string ToString() { return num.ToString(); } public static ModInteger operator +(ModInteger l, ModInteger r) { var n = l.num + r.num; if (n >= Mod) n -= Mod; return new ModInteger() { num = n }; } public static ModInteger operator -(ModInteger l, ModInteger r) { var n = l.num + Mod - r.num; if (n >= Mod) n -= Mod; return new ModInteger() { num = n }; } public static ModInteger operator *(ModInteger l, ModInteger r) { return new ModInteger(l.num * r.num); } public static ModInteger operator ^(ModInteger l, long r) { return ModInteger.Pow(l, r); } public static implicit operator ModInteger(long n) { return new ModInteger(n); } public static ModInteger Pow(ModInteger v, long k) { ModInteger ret = 1; var n = k; for (; n > 0; n >>= 1, v *= v) { if ((n & 1) == 1) ret = ret * v; } return ret; } } #endregion #region HLTreeGraph public class HLTreeGraph { public void Update(int from, int to, int val) { var f = go[from]; var t = go[to]; if (f.id == t.id) { f.seg.Add(pos[from], pos[to] + 1, val); } else { var ch = GetAncestorAt(t, f.depth + 1); var med = H[ch]; f.seg.Add(pos[from], pos[med.light.from] + 1, val); Update(med.light.to, to, val); } } public ModInteger Query(int from, int to) { var f = go[from]; var t = go[to]; if (f.id == t.id) { var val = f.seg.Query(pos[from], pos[to] + 1); return val; } else { var ch = GetAncestorAt(t, f.depth + 1); var med = H[ch]; var val = f.seg.Query(pos[from], pos[med.light.from] + 1); var val2 = Query(med.light.to, to); return val + val2; } } public int[] A, B; int N; List[] G; List H = new List(); int[] subTreeSize; int[] par; int[] pos; int[] depth; int[] ord; Chain[] go; int[,] hlpar; public HLTreeGraph(int n) { N = n; G = Enumerate(n, x => new List()); subTreeSize = new int[n]; pos = new int[n]; depth = new int[n]; par = new int[n]; go = new Chain[n]; ord = new int[n]; } public void AddEdge(int f, int t) { G[f].Add(new Edge(f, t)); G[t].Add(new Edge(t, f)); } #region impl public void Build(int root) { ComputeSubTreeSize(root); Decomposite(new Edge(-1, root), -1, 0, 0); BuildHLLCA(); } public void ComputeSubTreeSize(int root) { var ord = new int[N]; par[root] = -1; depth[root] = 0; var ptr = 0; var last = 0; ord[last++] = root; while (ptr < last) { var p = ord[ptr++]; foreach (var to in G[p]) { if (to.to != par[p]) { par[to.to] = p; depth[to.to] = depth[p] + 1; ord[last++] = to.to; } } } for (int i = N - 1; i > 0; i--) { subTreeSize[i] += 1; subTreeSize[par[i]] += subTreeSize[i]; } } public void Decomposite(Edge light, int prevId, int d, int lv) { var chain = new Chain() { light = light, id = H.Count, par = prevId, depth = lv }; H.Add(chain); var prev = light.from; var cur = light.to; while (cur != prev) { var next = cur; var max = 0; go[cur] = chain; pos[cur] = chain.heavy.Count; foreach (var to in G[cur]) { var t = to.to; if (t != prev) max = Math.Max(max, subTreeSize[t]); } foreach (var to in G[cur]) { var t = to.to; if (t == prev) continue; if (max == subTreeSize[t]) { //Debug.WriteLine("{0}->{1}", cur, t); max = 1 << 30; next = t; chain.heavy.Add(to); } else Decomposite(to, chain.id, d + 1, lv + 1); } prev = cur; cur = next; d++; } chain.init(this); } void BuildHLLCA() { hlpar = new int[8, H.Count]; for (int k = 0; k < 7; k++) for (int v = 0; v < H.Count; v++) hlpar[k, v] = -1; for (int i = 0; i < H.Count; i++) hlpar[0, i] = H[i].par; for (int k = 0; k < 7; k++) { for (int v = 0; v < H.Count; v++) if (hlpar[k, v] < 0) hlpar[k + 1, v] = -1; else hlpar[k + 1, v] = hlpar[k, hlpar[k, v]]; } } public int GetAncestorAt(Chain v, int d) { if (v.depth < d) throw new Exception(); for (int i = 0; i < 8; i++) if ((((v.depth - d) >> i) & 1) == 1) v = H[hlpar[i, v.id]]; return v.id; } public int GetLCA(int u, int v) { while (go[u].id != go[v].id) { if (go[u].depth < go[v].depth) v = go[v].light.from; else u = go[u].light.from; } if (depth[u] <= depth[v]) return u; else return v; } static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } #endregion } public class Chain { public Edge light; public List heavy = new List(); public int par; public int depth; public int id; public LazyRangeAddTree seg; public void init(HLTreeGraph G) { var a = new int[heavy.Count + 1]; var b = new int[heavy.Count + 1]; a[0] += G.A[light.to]; b[0] = G.B[light.to]; for (int i = 0; i < heavy.Count; i++) { a[i + 1] += G.A[heavy[i].to]; b[i + 1] += G.B[heavy[i].to]; } seg = new LazyRangeAddTree(heavy.Count + 1, a, b); } public override string ToString() { var s = new List(); s.Add(light.from); s.Add(light.to); foreach (var e in heavy) s.Add(e.to); return s.AsJoinedString("->"); } } #endregion #region TreeEdge public struct Edge { public int from, to; public Edge(int f, int t) { from = f; to = t; } public override string ToString() { return string.Format("{0}->{1}", from, to); } } #endregion #region LazyRangeAdd public class LazyRangeAddTree { int n; ModInteger[] sum, add, lazy; public LazyRangeAddTree(int size, int[] a, int[] b) { n = 1; while (n < size) n <<= 1; add = new ModInteger[n << 1]; sum = new ModInteger[n << 1]; for (int i = 0; i < a.Length; i++) { add[i + n] += b[i]; sum[i + n] += a[i]; } lazy = new ModInteger[n << 1]; for (int i = n - 1; i > 0; i--) { add[i] = add[i << 1] + add[(i << 1) + 1]; sum[i] = sum[i << 1] + sum[(i << 1) + 1]; } } private void lazyEval(int k, int a, int b) { if (lazy[k].num == 0) return; Add(a, (a + b) >> 1, lazy[k].num, k << 1, a, (a + b) >> 1); Add((a + b) >> 1, b, lazy[k].num, (k << 1) + 1, (a + b) >> 1, b); lazy[k] = 0; } private void eval(int k) { int l = k << 1, r = (k << 1) + 1; sum[k] = sum[l] + sum[r]; } public void Add(int a, int b, long v) { Add(a, b, v, 1, 0, n); } private void Add(int a, int b, long v, int k, int l, int r) { if (r <= a || b <= l) return; else if (a <= l && r <= b) { lazy[k] += v; sum[k] += add[k] * v; } else { lazyEval(k, l, r); Add(a, b, v, k << 1, l, (l + r) >> 1); Add(a, b, v, (k << 1) + 1, (l + r) >> 1, r); eval(k); } } public ModInteger Query(int a, int b) { return Query(a, b, 1, 0, n); } private ModInteger Query(int a, int b, int k, int l, int r) { if (r <= a || b <= l) return 0; if (a <= l && r <= b) return sum[k]; else { lazyEval(k, l, r); var vl = Query(a, b, k << 1, l, (l + r) >> 1); var vr = Query(a, b, (k << 1) + 1, (l + r) >> 1, r); eval(k); return vl + vr; } } } #endregion