Problem: You are given a directed weighted graph with n nodes and 2n - 2 edges. The nodes are labeled from 1 to n, while the edges are labeled from 1 to 2n - 2. The graph's edges can be split into two parts.

  * The first n - 1 edges will form a rooted spanning tree, with node 1 as the root. All these edges will point away from the root. 
  * The last n - 1 edges will be from node i to node 1, for all 2 ≤ i ≤ n. 



You are given q queries. There are two types of queries

  * 1 i w: Change the weight of the i-th edge to w
  * 2 u v: Print the length of the shortest path between nodes u to v



Given these queries, print the shortest path lengths.

Input

The first line of input will contain two integers n, q (2 ≤ n, q ≤ 200 000), the number of nodes, and the number of queries, respectively.

The next 2n - 2 integers will contain 3 integers ai, bi, ci, denoting a directed edge from node ai to node bi with weight ci.

The first n - 1 of these lines will describe a rooted spanning tree pointing away from node 1, while the last n - 1 of these lines will have bi = 1.

More specifically, 

  * The edges (a1, b1), (a2, b2), ... (an - 1, bn - 1) will describe a rooted spanning tree pointing away from node 1. 
  * bj = 1 for n ≤ j ≤ 2n - 2. 
  * an, an + 1, ..., a2n - 2 will be distinct and between 2 and n. 



The next q lines will contain 3 integers, describing a query in the format described in the statement.

All edge weights will be between 1 and 106.

Output

For each type 2 query, print the length of the shortest path in its own line.

Example

Input

5 9
1 3 1
3 2 2
1 4 3
3 5 4
5 1 5
3 1 6
2 1 7
4 1 8
2 1 1
2 1 3
2 3 5
2 5 2
1 1 100
2 1 3
1 8 30
2 4 2
2 2 4


Output

0
1
4
8
100
132
10

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
namespace fastIO {
bool IOerror = 0;
inline char nc() {
  static char buf[100005], *p1 = buf + 100005, *pend = buf + 100005;
  if (p1 == pend) {
    p1 = buf;
    pend = buf + fread(buf, 1, 100005, stdin);
    if (pend == p1) {
      IOerror = 1;
      return -1;
    }
  }
  return *p1++;
}
inline bool blank(char ch) {
  return ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t';
}
inline void read(int &x) {
  bool sign = 0;
  char ch = nc();
  x = 0;
  for (; blank(ch); ch = nc())
    ;
  if (IOerror) return;
  if (ch == '-') sign = 1, ch = nc();
  for (; ch >= '0' && ch <= '9'; ch = nc()) x = x * 10 + ch - '0';
  if (sign) x = -x;
}
inline void read(long long &x) {
  bool sign = 0;
  char ch = nc();
  x = 0;
  for (; blank(ch); ch = nc())
    ;
  if (IOerror) return;
  if (ch == '-') sign = 1, ch = nc();
  for (; ch >= '0' && ch <= '9'; ch = nc()) x = x * 10 + ch - '0';
  if (sign) x = -x;
}
inline void read(double &x) {
  bool sign = 0;
  char ch = nc();
  x = 0;
  for (; blank(ch); ch = nc())
    ;
  if (IOerror) return;
  if (ch == '-') sign = 1, ch = nc();
  for (; ch >= '0' && ch <= '9'; ch = nc()) x = x * 10 + ch - '0';
  if (ch == '.') {
    double tmp = 1;
    ch = nc();
    for (; ch >= '0' && ch <= '9'; ch = nc())
      tmp /= 10.0, x += tmp * (ch - '0');
  }
  if (sign) x = -x;
}
inline void read(char *s) {
  char ch = nc();
  for (; blank(ch); ch = nc())
    ;
  if (IOerror) return;
  for (; !blank(ch) && !IOerror; ch = nc()) *s++ = ch;
  *s = 0;
}
inline void read(char &c) {
  for (c = nc(); blank(c); c = nc())
    ;
  if (IOerror) {
    c = -1;
    return;
  }
}
inline void read1(int &x) {
  char ch;
  int bo = 0;
  x = 0;
  for (ch = getchar(); ch < '0' || ch > '9'; ch = getchar())
    if (ch == '-') bo = 1;
  for (; ch >= '0' && ch <= '9'; x = x * 10 + ch - '0', ch = getchar())
    ;
  if (bo) x = -x;
}
inline void read1(long long &x) {
  char ch;
  int bo = 0;
  x = 0;
  for (ch = getchar(); ch < '0' || ch > '9'; ch = getchar())
    if (ch == '-') bo = 1;
  for (; ch >= '0' && ch <= '9'; x = x * 10 + ch - '0', ch = getchar())
    ;
  if (bo) x = -x;
}
inline void read1(double &x) {
  char ch;
  int bo = 0;
  x = 0;
  for (ch = getchar(); ch < '0' || ch > '9'; ch = getchar())
    if (ch == '-') bo = 1;
  for (; ch >= '0' && ch <= '9'; x = x * 10 + ch - '0', ch = getchar())
    ;
  if (ch == '.') {
    double tmp = 1;
    for (ch = getchar(); ch >= '0' && ch <= '9';
         tmp /= 10.0, x += tmp * (ch - '0'), ch = getchar())
      ;
  }
  if (bo) x = -x;
}
inline void read1(char *s) {
  char ch = getchar();
  for (; blank(ch); ch = getchar())
    ;
  for (; !blank(ch); ch = getchar()) *s++ = ch;
  *s = 0;
}
inline void read1(char &c) {
  for (c = getchar(); blank(c); c = getchar())
    ;
}
inline void read2(int &x) { scanf("%d", &x); }
inline void read2(long long &x) { scanf("%lld", &x); }
inline void read2(double &x) { scanf("%lf", &x); }
inline void read2(char *s) { scanf("%s", s); }
inline void read2(char &c) { scanf(" %c", &c); }
inline void readln2(char *s) { gets(s); }
struct Ostream_fwrite {
  char *buf, *p1, *pend;
  Ostream_fwrite() {
    buf = new char[100005];
    p1 = buf;
    pend = buf + 100005;
  }
  void out(char ch) {
    if (p1 == pend) {
      fwrite(buf, 1, 100005, stdout);
      p1 = buf;
    }
    *p1++ = ch;
  }
  void print(int x) {
    static char s[15], *s1;
    s1 = s;
    if (!x) *s1++ = '0';
    if (x < 0) out('-'), x = -x;
    while (x) *s1++ = x % 10 + '0', x /= 10;
    while (s1-- != s) out(*s1);
  }
  void println(int x) {
    static char s[15], *s1;
    s1 = s;
    if (!x) *s1++ = '0';
    if (x < 0) out('-'), x = -x;
    while (x) *s1++ = x % 10 + '0', x /= 10;
    while (s1-- != s) out(*s1);
    out('\n');
  }
  void print(long long x) {
    static char s[25], *s1;
    s1 = s;
    if (!x) *s1++ = '0';
    if (x < 0) out('-'), x = -x;
    while (x) *s1++ = x % 10 + '0', x /= 10;
    while (s1-- != s) out(*s1);
  }
  void println(long long x) {
    static char s[25], *s1;
    s1 = s;
    if (!x) *s1++ = '0';
    if (x < 0) out('-'), x = -x;
    while (x) *s1++ = x % 10 + '0', x /= 10;
    while (s1-- != s) out(*s1);
    out('\n');
  }
  void print(double x, int y) {
    static long long mul[] = {1,
                              10,
                              100,
                              1000,
                              10000,
                              100000,
                              1000000,
                              10000000,
                              100000000,
                              1000000000,
                              10000000000LL,
                              100000000000LL,
                              1000000000000LL,
                              10000000000000LL,
                              100000000000000LL,
                              1000000000000000LL,
                              10000000000000000LL,
                              100000000000000000LL};
    if (x < -1e-12) out('-'), x = -x;
    x *= mul[y];
    long long x1 = (long long)floor(x);
    if (x - floor(x) >= 0.5) ++x1;
    long long x2 = x1 / mul[y], x3 = x1 - x2 * mul[y];
    print(x2);
    if (y > 0) {
      out('.');
      for (size_t i = 1; i < y && x3 * mul[i] < mul[y]; out('0'), ++i)
        ;
      print(x3);
    }
  }
  void println(double x, int y) {
    print(x, y);
    out('\n');
  }
  void print(char *s) {
    while (*s) out(*s++);
  }
  void println(char *s) {
    while (*s) out(*s++);
    out('\n');
  }
  void flush() {
    if (p1 != buf) {
      fwrite(buf, 1, p1 - buf, stdout);
      p1 = buf;
    }
  }
  ~Ostream_fwrite() { flush(); }
} Ostream;
inline void print(int x) { Ostream.print(x); }
inline void println(int x) { Ostream.println(x); }
inline void print(char x) { Ostream.out(x); }
inline void println(char x) {
  Ostream.out(x);
  Ostream.out('\n');
}
inline void print(long long x) { Ostream.print(x); }
inline void println(long long x) { Ostream.println(x); }
inline void print(double x, int y) { Ostream.print(x, y); }
inline void println(double x, int y) { Ostream.println(x, y); }
inline void print(char *s) { Ostream.print(s); }
inline void println(char *s) { Ostream.println(s); }
inline void println() { Ostream.out('\n'); }
inline void flush() { Ostream.flush(); }
char Out[100005], *o = Out;
inline void print1(int x) {
  static char buf[15];
  char *p1 = buf;
  if (!x) *p1++ = '0';
  if (x < 0) *o++ = '-', x = -x;
  while (x) *p1++ = x % 10 + '0', x /= 10;
  while (p1-- != buf) *o++ = *p1;
}
inline void println1(int x) {
  print1(x);
  *o++ = '\n';
}
inline void print1(long long x) {
  static char buf[25];
  char *p1 = buf;
  if (!x) *p1++ = '0';
  if (x < 0) *o++ = '-', x = -x;
  while (x) *p1++ = x % 10 + '0', x /= 10;
  while (p1-- != buf) *o++ = *p1;
}
inline void println1(long long x) {
  print1(x);
  *o++ = '\n';
}
inline void print1(char c) { *o++ = c; }
inline void println1(char c) {
  *o++ = c;
  *o++ = '\n';
}
inline void print1(char *s) {
  while (*s) *o++ = *s++;
}
inline void println1(char *s) {
  print1(s);
  *o++ = '\n';
}
inline void println1() { *o++ = '\n'; }
inline void flush1() {
  if (o != Out) {
    if (*(o - 1) == '\n') *--o = 0;
    puts(Out);
  }
}
struct puts_write {
  ~puts_write() { flush1(); }
} _puts;
inline void print2(int x) { printf("%d", x); }
inline void println2(int x) { printf("%d\n", x); }
inline void print2(char x) { printf("%c", x); }
inline void println2(char x) { printf("%c\n", x); }
inline void print2(long long x) { printf("%lld", x); }
inline void println2(long long x) {
  print2(x);
  printf("\n");
}
inline void println2() { printf("\n"); }
};  // namespace fastIO
int n, q, u[404000], v[404000], w[404000], bak[404000] = {0};
struct R {
  int to, val, nex;
} r[202000];
int hea[202000] = {0}, cnt = 1;
int df1[202000], df2[202000], dft = 0;
long long an, ans;
namespace D {
long long d[202000];
inline void RE() { memset(d, 0, sizeof d); }
inline void add(int x, int v) {
  for (; x <= n; x += x & (-x)) d[x] += v;
}
inline void A(int st, int en, int val) {
  add(st, val);
  add(en + 1, -val);
}
inline long long Q(int x) {
  long long t = 0;
  for (; x > 0; x -= x & -x) t += d[x];
  return t;
}
}  // namespace D
namespace tr {
long long mn[808000], laz[808000];
inline void U(int x) { mn[x] = min(mn[x << 1], mn[x << 1 | 1]); }
inline void D(int x) {
  if (!laz[x]) return;
  mn[x << 1] += laz[x];
  laz[x << 1] += laz[x];
  mn[x << 1 | 1] += laz[x];
  laz[x << 1 | 1] += laz[x];
  U(x);
  laz[x] = 0;
}
inline void B(int x, int l, int r) {
  laz[x] = 0;
  if (l == r) {
    mn[x] = D::Q(l) + bak[l];
    return;
  }
  int mid = (l + r) >> 1;
  B(x << 1, l, mid);
  B(x << 1 | 1, mid + 1, r);
  U(x);
}
inline void RE() { B(1, 1, n); }
inline long long que(int x, int l, int r, int st, int en) {
  if (st > en) return (1e16);
  if (l == st && r == en) return mn[x];
  D(x);
  int mid = (l + r) >> 1;
  return min(que(x << 1, l, mid, max(st, l), min(en, mid)),
             que(x << 1 | 1, mid + 1, r, max(st, mid + 1), min(en, r)));
}
inline long long Q(int st, int en) { return que(1, 1, n, st, en); }
inline void chg(int x, int l, int r, int st, int en, int val) {
  if (st > en) return;
  if (l == st && r == en) {
    mn[x] += val;
    laz[x] += val;
    return;
  }
  D(x);
  int mid = (l + r) >> 1;
  chg(x << 1, l, mid, max(st, l), min(en, mid), val);
  chg(x << 1 | 1, mid + 1, r, max(st, mid + 1), min(en, r), val);
  U(x);
}
inline void C(int st, int en, int val) { chg(1, 1, n, st, en, val); }
}  // namespace tr
inline void dfs(int x) {
  df1[x] = ++dft;
  int y;
  for (int i = hea[x]; i > 0; i = r[i].nex) {
    y = r[i].to;
    dfs(y);
  }
  df2[x] = dft;
}
int main() {
  D::RE();
  fastIO::read(n);
  fastIO::read(q);
  int x, y, z;
  for (int i = 1; i < n; i++) {
    fastIO::read(u[i]);
    fastIO::read(v[i]);
    fastIO::read(w[i]);
    r[++cnt] = (R){v[i], w[i], hea[u[i]]};
    hea[u[i]] = cnt;
  }
  dfs(1);
  for (int i = n; i <= n * 2 - 2; i++) {
    fastIO::read(u[i]);
    fastIO::read(v[i]);
    fastIO::read(w[i]);
    bak[df1[u[i]]] = w[i];
  }
  for (int i = 1; i < n; i++) {
    D::A(df1[v[i]], df2[v[i]], w[i]);
  }
  tr::RE();
  for (int t; q--;) {
    fastIO::read(t);
    fastIO::read(x);
    fastIO::read(y);
    if (t == 1) {
      if (x < n) {
        D::A(df1[v[x]], df2[v[x]], y - w[x]);
        tr::C(df1[v[x]], df2[v[x]], y - w[x]);
        w[x] = y;
      } else {
        tr::C(df1[u[x]], df1[u[x]], y - bak[df1[u[x]]]);
        bak[df1[u[x]]] = y;
      }
    } else {
      if (df1[x] <= df1[y] && df2[x] >= df2[y]) {
        ans = D::Q(df1[y]) - D::Q(df1[x]);
      } else {
        ans = tr::Q(df1[x], df2[x]) - D::Q(df1[x]) + D::Q(df1[y]);
      }
      fastIO::println(ans);
    }
  }
}