#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
    int n = a.size();
    vector<T> b(n);
    for (int i = 0; i < n; i++) b[i] = a[ord[i]];
    swap(a, b);
}

template <typename T>
T floor(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? x / y : (x - y + 1) / y);
}

template <typename T>
T ceil(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? (x + y - 1) / y : x / y);
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(15);
    }
} io_setup;

constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;

// sum
template <typename T>
struct Plus_Monoid {
    using V = T;
    static constexpr V merge(const V &a, const V &b) { return a + b; };
    static const V id;
};

template <typename T>
const T Plus_Monoid<T>::id = 0;

// prod
template <typename T>
struct Product_Monoid {
    using V = T;
    static constexpr V merge(const V &a, const V &b) { return a * b; };
    static const V id;
};

template <typename T>
const T Product_Monoid<T>::id = 1;

// min
template <typename T>
struct Min_Monoid {
    using V = T;
    static constexpr V merge(const V &a, const V &b) { return min(a, b); };
    static const V id;
};

template <typename T>
constexpr T Min_Monoid<T>::id = numeric_limits<T>::max() / 2;

// max
template <typename T>
struct Max_Monoid {
    using V = T;
    static constexpr V merge(V a, V b) { return max(a, b); };
    static const V id;
};

template <typename T>
constexpr T Max_Monoid<T>::id = -(numeric_limits<T>::max() / 2);

// 代入
template <typename T>
struct Update_Monoid {
    using V = T;
    static constexpr V merge(const V &a, const V &b) {
        if (a == id) return b;
        if (b == id) return a;
        return b;
    }
    static const V id;
};

template <typename T>
constexpr T Update_Monoid<T>::id = numeric_limits<T>::max();

// min count (T：最大値の型、S：個数の型)
template <typename T, typename S>
struct Min_Count_Monoid {
    using V = pair<T, S>;
    static constexpr V merge(const V &a, const V &b) {
        if (a.first < b.first) return a;
        if (a.first > b.first) return b;
        return V(a.first, a.second + b.second);
    }
    static const V id;
};

template <typename T, typename S>
constexpr pair<T, S> Min_Count_Monoid<T, S>::id = make_pair(numeric_limits<T>::max() / 2, 0);

// max count (T：最大値の型、S：個数の型)
template <typename T, typename S>
struct Max_Count_Monoid {
    using V = pair<T, S>;
    static constexpr V merge(const V &a, const V &b) {
        if (a.first > b.first) return a;
        if (a.first < b.first) return b;
        return V(a.first, a.second + b.second);
    }
    static const V id;
};

template <typename T, typename S>
constexpr pair<T, S> Max_Count_Monoid<T, S>::id = make_pair(-(numeric_limits<T>::max() / 2), 0);

// 一次関数 ax+b の合成 (左から順に作用)
template <typename T>
struct Affine_Monoid {
    using V = pair<T, T>;
    static constexpr V merge(const V &a, const V &b) { return V(a.first * b.first, a.second * b.first + b.second); };
    static const V id;
};

template <typename T>
const pair<T, T> Affine_Monoid<T>::id = make_pair(1, 0);

// モノイドの直積
template <typename Monoid_1, typename Monoid_2>
struct Cartesian_Product_Monoid {
    using V1 = typename Monoid_1::V;
    using V2 = typename Monoid_2::V;
    using V = pair<V1, V2>;
    static constexpr V merge(const V &a, const V &b) { return V(Monoid_1::merge(a.first, b.first), Monoid_2::merge(a.second, b.second)); }
    static const V id;
};

template <typename Monoid_1, typename Monoid_2>
const pair<typename Monoid_1::V, typename Monoid_2::V> Cartesian_Product_Monoid<Monoid_1, Monoid_2>::id = make_pair(Monoid_1::id, Monoid_2::id);

// range add range min
template <typename T>
struct Min_Plus_Acted_Monoid {
    using Monoid = Min_Monoid<T>;
    using Operator = Plus_Monoid<T>;
    using M = T;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return a + b; };
};

// range add range max
template <typename T>
struct Max_Plus_Acted_Monoid {
    using Monoid = Max_Monoid<T>;
    using Operator = Plus_Monoid<T>;
    using M = T;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return a + b; };
};

// range add range min count (T：最小値の型、S：個数の型)
template <typename T, typename S>
struct Min_Count_Add_Acted_Monoid {
    using Monoid = Min_Count_Monoid<T, S>;
    using Operator = Plus_Monoid<T>;
    using M = pair<T, S>;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return make_pair(a.first + b, a.second); };
};

// range add range max count (T：最大値の型、S：個数の型)
template <typename T, typename S>
struct Max_Count_Add_Acted_Monoid {
    using Monoid = Max_Count_Monoid<T, S>;
    using Operator = Plus_Monoid<T>;
    using M = pair<T, S>;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return make_pair(a.first + b, a.second); };
};

// range add range sum
template <typename T>
struct Plus_Plus_Acted_Monoid {
    using Monoid = Cartesian_Product_Monoid<Plus_Monoid<T>, Plus_Monoid<int>>;
    using Operator = Plus_Monoid<T>;
    using M = pair<T, int>;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return M(a.first + b * a.second, a.second); }
};

// range update range sum
template <typename T>
struct Plus_Update_Acted_Monoid {
    using Monoid = Cartesian_Product_Monoid<Plus_Monoid<T>, Plus_Monoid<int>>;
    using Operator = Update_Monoid<T>;
    using M = pair<T, int>;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return b == Operator::id ? a : M(b * a.second, a.second); }
};

// range update range min
template <typename T>
struct Min_Update_Acted_Monoid {
    using Monoid = Min_Monoid<T>;
    using Operator = Update_Monoid<T>;
    using M = T;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return b == Operator::id ? a : b; }
};

// range update range max
template <typename T>
struct Max_Update_Acted_Monoid {
    using Monoid = Max_Monoid<T>;
    using Operator = Update_Monoid<T>;
    using M = T;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return b == Operator::id ? a : b; }
};

// range affine range sum
template <typename T>
struct Plus_Affine_Acted_Monoid {
    using Monoid = Cartesian_Product_Monoid<Plus_Monoid<T>, Plus_Monoid<T>>;
    using Operator = Affine_Monoid<T>;
    using M = pair<T, T>;
    using O = pair<T, T>;
    static constexpr M merge(const M &a, const O &b) { return M(b.first * a.first + b.second * a.second, a.second); };
};

template <typename Acted_Monoid>
struct Lazy_Segment_Tree {
    using Monoid = typename Acted_Monoid::Monoid;
    using Operator = typename Acted_Monoid::Operator;
    using M = typename Monoid::V;
    using O = typename Operator::V;
    int n, m, height;
    vector<M> seg;
    vector<O> lazy;

    // f(f(a,b),c) = f(a,f(b,c)), f(e1,a) = f(a,e1) = a
    // h(h(p,q),r) = h(p,h(q,r)), h(e2,p) = h(p,e2) = p
    // g(f(a,b),p) = f(g(a,p),g(b,p))
    // g(g(a,p),q) = g(a,h(p,q))

    Lazy_Segment_Tree(const vector<M> &v) : n(v.size()) {
        m = 1, height = 0;
        while (m < n) m <<= 1, height++;
        seg.assign(2 * m, Monoid::id), lazy.assign(2 * m, Operator::id);
        copy(begin(v), end(v), begin(seg) + m);
        build();
    }

    Lazy_Segment_Tree(int n, M x = Monoid::id) : Lazy_Segment_Tree(vector<M>(n, x)) {}

    void set(int i, const M &x) { seg[m + i] = x; }

    void build() {
        for (int i = m - 1; i > 0; i--) seg[i] = Monoid::merge(seg[2 * i], seg[2 * i + 1]);
    }

    inline M reflect(int i) const { return Acted_Monoid::merge(seg[i], lazy[i]); }

    inline void recalc(int i) {
        while (i >>= 1) seg[i] = Monoid::merge(reflect(2 * i), reflect(2 * i + 1));
    }

    inline void eval(int i) {
        lazy[2 * i] = Operator::merge(lazy[2 * i], lazy[i]);
        lazy[2 * i + 1] = Operator::merge(lazy[2 * i + 1], lazy[i]);
        seg[i] = reflect(i);
        lazy[i] = Operator::id;
    }

    inline void thrust(int i) {
        for (int j = height; j > 0; j--) eval(i >> j);
    }

    void update(int l, int r, const O &x) {
        l = max(l, 0), r = min(r, n);
        if (l >= r) return;
        l += m, r += m;
        thrust(l), thrust(r - 1);
        int a = l, b = r;
        while (l < r) {
            if (l & 1) lazy[l] = Operator::merge(lazy[l], x), l++;
            if (r & 1) r--, lazy[r] = Operator::merge(lazy[r], x);
            l >>= 1, r >>= 1;
        }
        recalc(a), recalc(b - 1);
    }

    M query(int l, int r) {
        l = max(l, 0), r = min(r, n);
        if (l >= r) return Monoid::id;
        l += m, r += m;
        thrust(l), thrust(r - 1);
        M L = Monoid::id, R = Monoid::id;
        while (l < r) {
            if (l & 1) L = Monoid::merge(L, reflect(l++));
            if (r & 1) R = Monoid::merge(reflect(--r), R);
            l >>= 1, r >>= 1;
        }
        return Monoid::merge(L, R);
    }

    M operator[](int i) { return query(i, i + 1); }

    template <typename C>
    int find_subtree(int i, const C &check, M &x, int type) {
        while (i < m) {
            eval(i);
            M nxt = type ? Monoid::merge(reflect(2 * i + type), x) : Monoid::merge(x, reflect(2 * i + type));
            if (check(nxt)) {
                i = 2 * i + type;
            } else {
                x = nxt;
                i = 2 * i + (type ^ 1);
            }
        }
        return i - m;
    }

    // check(区間 [l,r] での演算結果) を満たす最小の r (なければ n)
    template <typename C>
    int find_first(int l, const C &check) {
        M L = Monoid::id;
        int a = l + m, b = 2 * m;
        thrust(a);
        while (a < b) {
            if (a & 1) {
                M nxt = Monoid::merge(L, reflect(a));
                if (check(nxt)) return find_subtree(a, check, L, 0);
                L = nxt;
                a++;
            }
            a >>= 1, b >>= 1;
        }
        return n;
    }

    // check(区間 [l,r) での演算結果) を満たす最大の l (なければ -1)
    template <typename C>
    int find_last(int r, const C &check) {
        M R = Monoid::id;
        int a = m, b = r + m;
        thrust(b - 1);
        while (a < b) {
            if ((b & 1) || a == 1) {
                M nxt = Monoid::merge(reflect(--b), R);
                if (check(nxt)) return find_subtree(b, check, R, 1);
                R = nxt;
            }
            a >>= 1, b >>= 1;
        }
        return -1;
    }
};

template <bool directed = false>
struct Euler_Tour_Subtree {
    struct edge {
        int to, id;
        edge(int to, int id) : to(to), id(id) {}
    };

    vector<vector<edge>> es;
    vector<int> l, r; // 部分木 i は区間 [l[i],r[i]) に対応する。また、頂点 i は l[i] に対応する。
    const int n;
    int m;

    Euler_Tour_Subtree(int n) : es(n), l(n), r(n), n(n), m(0) {}

    void add_edge(int from, int to) {
        es[from].emplace_back(to, m);
        if (!directed) es[to].emplace_back(from, m);
        m++;
    }

    void _dfs(int now, int pre, int &cnt) {
        l[now] = cnt++;
        for (auto &e : es[now]) {
            if (e.to != pre) _dfs(e.to, now, cnt);
        }
        r[now] = cnt;
    }

    void build(int root = 0) {
        int cnt = 0;
        _dfs(root, -1, cnt);
    }
};

template <bool directed = false>
struct Heavy_Light_Decomposition {
    struct edge {
        int to, id;
        edge(int to, int id) : to(to), id(id) {}
    };

    vector<vector<edge>> es;
    vector<int> par, si, depth;
    vector<int> root;       // 属する連結成分の根
    vector<int> id_v, id_e; // 各頂点、各辺が一列に並べたときに何番目に相当するか (辺の番号は 1,2,...,n-1 となることに注意)
    vector<int> vs;
    const int n;
    int m;

    Heavy_Light_Decomposition(int n) : es(n), par(n), si(n, 1), depth(n, -1), root(n), id_v(n), id_e(n - 1), vs(n), n(n), m(0) {}

    void add_edge(int from, int to) {
        es[from].emplace_back(to, m);
        if (!directed) es[to].emplace_back(from, m);
        m++;
    }

    int bfs_sz(int r, int s) {
        int t = s;
        queue<int> que;
        que.push(r);
        depth[r] = 0;
        vs[t++] = r;
        while (!que.empty()) {
            int i = que.front();
            que.pop();
            for (auto &e : es[i]) {
                if (depth[e.to] != -1) continue;
                par[e.to] = i;
                depth[e.to] = depth[i] + 1;
                vs[t++] = e.to;
                que.push(e.to);
            }
        }
        for (int i = t - 1; i >= s; i--) {
            for (auto &e : es[vs[i]]) {
                if (e.to != par[vs[i]]) si[vs[i]] += si[e.to];
            }
        }
        return t;
    }

    void bfs_hld(int r, int s) {
        id_v[r] = s;
        root[r] = r;
        queue<int> que;
        que.push(r);
        while (!que.empty()) {
            int i = que.front();
            que.pop();
            edge heavy = {-1, -1};
            int ma = 0;
            for (auto &e : es[i]) {
                if (e.to == par[i]) continue;
                if (ma < si[e.to]) ma = si[e.to], heavy = e;
            }
            int cnt = id_v[i] + 1;
            if (heavy.id != -1) {
                root[heavy.to] = root[i];
                id_e[heavy.id] = cnt;
                id_v[heavy.to] = cnt;
                que.push(heavy.to);
                cnt += si[heavy.to];
            }
            for (auto &e : es[i]) {
                if (e.to == par[i] || e.id == heavy.id) continue;
                root[e.to] = e.to;
                id_e[e.id] = cnt;
                id_v[e.to] = cnt;
                que.push(e.to);
                cnt += si[e.to];
            }
        }
    }

    void decompose() {
        int s = 0;
        for (int i = 0; i < n; i++) {
            if (depth[i] != -1) continue;
            int t = bfs_sz(i, s);
            bfs_hld(i, s);
            s = t;
        }
        for (int i = 0; i < n; i++) vs[id_v[i]] = i;
    }

    int lca(int u, int v) {
        while (root[u] != root[v]) {
            if (depth[root[u]] > depth[root[v]]) swap(u, v);
            v = par[root[v]];
        }
        if (depth[u] > depth[v]) swap(u, v);
        return u;
    }

    int dist(int u, int v) { return depth[u] + depth[v] - depth[lca(u, v)] * 2; }

    // u の k 個前の祖先
    int ancestor(int u, int k) {
        if (k > depth[u]) return -1;
        while (k > 0) {
            int r = root[u];
            int l = depth[u] - depth[r];
            if (k <= l) return vs[id_v[r] + l - k];
            u = par[r];
            k -= l + 1;
        }
        return u;
    }

    // u から v の方向へ k 回移動
    int move(int u, int v, int k) {
        int w = lca(u, v);
        int l = depth[u] + depth[v] - depth[w] * 2;
        if (k > l) return -1;
        if (k <= depth[u] - depth[w]) return ancestor(u, k);
        return ancestor(v, l - k);
    }

    // パスに対応する区間たちを列挙
    vector<pair<int, int>> get_path(int u, int v, bool use_edge = false) {
        vector<pair<int, int>> ret;
        while (root[u] != root[v]) {
            if (depth[root[u]] > depth[root[v]]) swap(u, v);
            ret.emplace_back(id_v[root[v]], id_v[v] + 1);
            v = par[root[v]];
        }
        if (depth[u] > depth[v]) swap(u, v);
        ret.emplace_back(id_v[u] + use_edge, id_v[v] + 1);
        return ret;
    }

    // クエリが非可換の場合 (l > r なら子から親方向で [r,l)、l < r なら親から子方向で [l,r))
    vector<pair<int, int>> get_path_noncommutative(int u, int v, bool use_edge = false) {
        vector<pair<int, int>> l, r;
        while (root[u] != root[v]) {
            if (depth[root[u]] > depth[root[v]]) {
                l.emplace_back(id_v[u] + 1, id_v[root[u]]);
                u = par[root[u]];
            } else {
                r.emplace_back(id_v[root[v]], id_v[v] + 1);
                v = par[root[v]];
            }
        }
        if (depth[u] > depth[v]) {
            l.emplace_back(id_v[u] + 1, id_v[v] + use_edge);
        } else {
            r.emplace_back(id_v[u] + use_edge, id_v[v] + 1);
        }
        reverse(begin(r), end(r));
        for (auto &e : r) l.push_back(e);
        return l;
    }
};

template <typename Acted_Monoid, bool use_edge, bool directed = false>
struct HLD_Lazy_Segment_Tree : Heavy_Light_Decomposition<directed> {
    using HLD = Heavy_Light_Decomposition<directed>;
    using Monoid = typename Acted_Monoid::Monoid;
    using Operator = typename Acted_Monoid::Operator;
    using M = typename Monoid::V;
    using O = typename Operator::V;
    Lazy_Segment_Tree<Acted_Monoid> seg;
    vector<M> v;
    const int n;

    HLD_Lazy_Segment_Tree(const vector<M> &v) : HLD((int)v.size()), seg((int)v.size()), v(v), n((int)v.size()) {}

    HLD_Lazy_Segment_Tree(int n, M x = Monoid::id) : HLD(n), seg(n), v(n, x), n(n) {}

    void set(int i, const M &x) { v[i] = x; }

    void build() {
        this->decompose();
        if (use_edge) {
            for (int i = 0; i < n - 1; i++) seg.set(this->id_e[i], v[i]);
        } else {
            for (int i = 0; i < n; i++) seg.set(this->id_v[i], v[i]);
        }
        seg.build();
    }

    void update(int u, int v, const O &x) {
        for (auto [l, r] : this->get_path(u, v, use_edge)) seg.update(l, r, x);
    }

    M query(int u, int v) {
        M ret = Monoid::id;
        for (auto [l, r] : this->get_path(u, v, use_edge)) ret = Monoid::merge(ret, seg.query(l, r));
        return ret;
    }

    M operator[](int i) { return seg[(use_edge ? this->id_e : this->id_v)[i]]; }
};

template <typename Acted_Monoid, bool use_edge, bool directed = false>
struct HLD_Lazy_Segment_Tree_Noncommutative : Heavy_Light_Decomposition<directed> {
    using HLD = Heavy_Light_Decomposition<directed>;
    using Monoid = typename Acted_Monoid::Monoid;
    using Operator = typename Acted_Monoid::Operator;
    using M = typename Monoid::V;
    using O = typename Operator::V;
    Lazy_Segment_Tree<Acted_Monoid> seg1, seg2;
    vector<M> v;
    const int n;

    HLD_Lazy_Segment_Tree_Noncommutative(const vector<M> &v) : HLD((int)v.size()), seg1((int)v.size()), seg2((int)v.size()), v(v), n((int)v.size()) {}

    HLD_Lazy_Segment_Tree_Noncommutative(int n, M x = Monoid::id) : HLD(n), seg1(n), seg2(n), v(n, x), n(n) {}

    void set(int i, const M &x) { v[i] = x; }

    void build() {
        this->decompose();
        if (use_edge) {
            for (int i = 0; i < n - 1; i++) {
                seg1.set(this->id_e[i], v[i]);
                seg2.set(n - 1 - this->id_e[i], v[i]);
            }
        } else {
            for (int i = 0; i < n; i++) {
                seg1.set(this->id_v[i], v[i]);
                seg2.set(n - 1 - this->id_v[i], v[i]);
            }
        }
        seg1.build(), seg2.build();
    }

    void update(int u, int v, const O &x) {
        for (auto [l, r] : this->get_path(u, v, use_edge)) {
            seg1.update(l, r, x);
            seg2.update(n - r, n - l, x);
        }
    }

    M query(int u, int v) {
        M ret = Monoid::id;
        for (auto [l, r] : this->get_path_noncommutative(u, v, use_edge)) {
            if (l > r) {
                ret = Monoid::merge(ret, seg2.query(n - l, n - r));
            } else {
                ret = Monoid::merge(ret, seg1.query(l, r));
            }
        }
        return ret;
    }

    M operator[](int i) { return seg1[(use_edge ? this->id_e : this->id_v)[i]]; }
};

void solve() {
    int N, Q;
    cin >> N >> Q;

    HLD_Lazy_Segment_Tree<Min_Plus_Acted_Monoid<ll>, false, false> seg(N);
    Euler_Tour_Subtree G(N);

    vector<int> u(N - 1), v(N - 1);
    vector<ll> c(N - 1);
    rep(i, N - 1) {
        cin >> u[i] >> v[i] >> c[i];
        u[i]--, v[i]--;
        seg.add_edge(u[i], v[i]);
        G.add_edge(u[i], v[i]);
    }

    seg.build();
    G.build();

    vector<int> iv(N, -1);
    rep(i, N) iv[seg.id_v[i]] = i;

    vector<ll> d(N, INF);

    rep(i, N - 1) {
        if (seg.depth[u[i]] > seg.depth[v[i]]) swap(u[i], v[i]);
        seg.update(v[i], v[i], -(1LL << 62) + 1 + c[i]);
        d[v[i]] = c[i];
    }

    // print(d);

    Lazy_Segment_Tree<Plus_Update_Acted_Monoid<int>> seg2(vector<pii>(N, pii(1, 1)));

    auto check = [&](ll x) { return x <= 0; };

    while (Q--) {
        int t;
        cin >> t;

        if (t == 1) {
            int i;
            ll x;
            cin >> i >> x;
            i--;
            seg.update(0, i, -x);
            // cout << "! " << seg.query(0, i) << '\n';
            for (auto [l, r] : seg.get_path(0, i)) {
                if (seg.seg.query(l, r) <= 0) {
                    int j = seg.seg.find_last(r, check);
                    int id = iv[j];
                    // assert(seg.id_v[j] == id);
                    seg2.update(G.l[id], G.r[id], 0);
                    ll w = d[id] - seg.seg[j];
                    // cout << "? " << j MM id + 1 MM w << '\n';
                    seg.update(0, id, w);
                }
            }
        } else {
            cout << seg2.query(0, N).first << '\n';
        }
    }
}

int main() {
    int T = 1;
    // cin >> T;
    while (T--) solve();
}