#include <bits/stdc++.h>

using i64 = long long;

constexpr i64 inf = 1E18;

struct Info {
    i64 ans = 0;
    i64 len = -inf;
    i64 vl = -inf;
    i64 vr = -inf;
};

constexpr int N = 1 << 19;

Info info[N];

Info operator+(const Info &a, const Info &b) {
    if (a.vl < 0) {
        return b;
    }
    if (b.vl < 0) {
        return a;
    }
    Info c;
    c.ans = std::max({a.ans, b.ans, a.vr + b.vl});
    c.len = std::max(-inf, a.len + b.len);
    c.vl = std::max(a.vl, a.len + b.vl);
    c.vr = std::max(b.vr, a.vr + b.len);
    return c;
}

Info query(int p, int l, int r, int x, int y) {
    if (l >= y || r <= x) {
        return {};
    }
    if (l >= x && r <= y) {
        return info[p];
    }
    int m = (l + r) / 2;
    return query(2 * p, l, m, x, y) + query(2 * p + 1, m, r, x, y);
}

void pull(int p) {
    info[p] = info[2 * p] + info[2 * p + 1];
}

void modify(int p, int l, int r, int x, const Info &v) {
    if (r - l == 1) {
        info[p] = v;
        return;
    }
    int m = (l + r) / 2;
    if (x < m) {
        modify(2 * p, l, m, x, v);
    } else {
        modify(2 * p + 1, m, r, x, v);
    }
    pull(p);
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    int n, q;
    std::cin >> n >> q;
    
    std::vector<int> a(n);
    for (int i = 0; i < n; i++) {
        std::cin >> a[i];
    }
    
    std::vector<int> p(n);
    p[0] = -1;
    for (int i = 1; i < n; i++) {
        std::cin >> p[i];
        p[i]--;
    }
    
    std::vector<int> c(n);
    for (int i = 1; i < n; i++) {
        std::cin >> c[i];
    }
    
    std::vector<int> w(n);
    for (int i = 1; i < n; i++) {
        std::cin >> w[i];
    }
    
    std::vector<int> dep(n), siz(n), in(n), top(n), bot(n);
    std::vector<std::vector<int>> adj(n);
    for (int i = 1; i < n; i++) {
        adj[p[i]].push_back(i);
    }
    auto dfs1 = [&](auto self, int x) -> void {
        siz[x] = 1;
        for (auto &y : adj[x]) {
            dep[y] = dep[x] + 1;
            self(self, y);
            siz[x] += siz[y];
            if (siz[y] > siz[adj[x][0]]) {
                std::swap(y, adj[x][0]);
            }
        }
    };
    dfs1(dfs1, 0);
    
    std::vector<std::multiset<std::pair<std::pair<int, int>, i64>>> chain(n);
    std::vector<std::multiset<std::pair<int, i64>>> val(n);
    
    auto get = [&](int x = 0) {
        return query(1, 0, n, in[x], in[bot[x]] + 1);
    };
    
    auto getmax = [&](const auto &s, const auto &v, int cnt = 1) {
        i64 ans = 0;
        auto it = s.upper_bound({v, inf});
        while (cnt-- && it != s.begin()) {
            it--;
            if (it->first == v) {
                ans += it->second;
            }
        }
        return ans;
    };
    
    auto add = [&](int x, int a, int c, i64 v) {
        i64 res = getmax(chain[x], std::make_pair(a, c), 2);
        val[x].extract({a, res});
        chain[x].emplace(std::make_pair(a, c), v);
        res = getmax(chain[x], std::make_pair(a, c), 2);
        if (res) {
            val[x].emplace(a, res);
        }
    };
    
    auto del = [&](int x, int a, int c, i64 v) {
        i64 res = getmax(chain[x], std::make_pair(a, c), 2);
        val[x].extract({a, res});
        chain[x].extract({std::make_pair(a, c), v});
        res = getmax(chain[x], std::make_pair(a, c), 2);
        if (res) {
            val[x].emplace(a, res);
        }
    };
    
    auto insert = [&](int x) {
        if (!x) {
            return;
        }
        int y = p[x];
        auto res = get(x);
        add(y, a[x], c[x], res.vl);
        if (res.ans) {
            val[y].emplace(-1, res.ans);
        }
    };
    
    auto erase = [&](int x) {
        if (!x) {
            return;
        }
        int y = p[x];
        auto res = get(x);
        del(y, a[x], c[x], res.vl);
        if (res.ans) {
            val[y].extract({-1, res.ans});
        }
    };
    
    auto update = [&](int x) {
        Info v;
        v.ans = std::max(getmax(val[x], a[x]), getmax(val[x], -1));
        if (!adj[x].empty()) {
            int y = adj[x][0];
            if (a[x] == a[y]) {
                v.vr = getmax(chain[x], std::make_pair(a[y], c[y]));
            }
            if (a[y] == a[x] && c[y] == c[x]) {
                v.len = w[x];
            }
        }
        v.vl = w[x] + getmax(chain[x], std::make_pair(a[x], c[x]));
        modify(1, 0, n, in[x], v);
    };
    
    int cur = 0;
    auto dfs2 = [&](auto self, int x) -> void {
        in[x] = cur++;
        for (auto y : adj[x]) {
            top[y] = y == adj[x][0] ? top[x] : y;
            self(self, y);
            if (y != adj[x][0]) {
                insert(y);
            }
        }
        bot[x] = adj[x].empty() ? x : bot[adj[x][0]];
        update(x);
    };
    dfs2(dfs2, 0);
    
    auto change = [&](int x, int y) {
        for (int i = x; i != -1; i = p[top[i]]) {
            erase(top[i]);
        }
        a[x] = y;
        if (top[x] != x) {
            update(p[x]);
        }
        for (int i = x; i != -1; i = p[top[i]]) {
            update(i);
            insert(top[i]);
        }
    };
    
    auto answer = [&]() {
        std::cout << get().ans << "\n";
    };
    
    answer();
    while (q--) {
        int x, y;
        std::cin >> x >> y;
        x--;
        
        change(x, y);
        
        answer();
    }
    
    return 0;
}