[PCCA 2020 pC]

#include <bits/stdc++.h>
using namespace std;

#define int long long

#define fastIO() ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)

const int maxn = 1 << 18;

vector<int> seg(2*maxn);

void build(vector<int> a, int len) {
    for (int i = 0; i < len; ++i) {
        seg[maxn + i] = a[i];
    }
    for (int i = maxn-1; i >= 1; --i) {
        seg[i] = max(seg[i<<1], seg[i<<1|1]);
    }
}

int RMax(int L, int R, int now = 1, int nL = 0, int nR = maxn-1) {
    if (L > nR or R < nL) return 0;
    if (nR <= R and nL >= L) return seg[now];
    return max(RMax(L, R, now*2  ,  nL        , (nL+nR)/2),
               RMax(L, R, now*2+1, (nL+nR)/2+1,  nR      ));
}

int32_t main() {
    fastIO();

    int n, m, ans(0);
    cin >> n >> m;

    vector<int> a(n), b(m), Ans;
    vector<bool> now(n, 1);
    for (auto &x : a) cin >> x;
    for (auto &x : b) cin >> x, now[--x] = 0;
    reverse(b.begin(), b.end());

    build(a, n);

    map<int, int> LtoR, RtoL;
    int nL = 0, nR;
    for (int i = 0; i < n; ++i) {
        while (i < n and now[i]) ++i;
        nR = i - 1;
        // cout << nL << ", " << nR << "\n";
        if (nL <= nR) LtoR[nL] = nR, RtoL[nR] = nL;
        nL = i + 1;
    }

    for (auto x : LtoR) {
        ans = max(ans, (x.second-x.first+1) * RMax(x.first, x.second));
    }

    int Lnum, Rnum;
    for (auto x : b) {
        Ans.push_back(ans);
        if (x == 0 and now[1]) {
            Lnum = 0;
            Rnum = LtoR[1];
            LtoR[Lnum] = Rnum;
            RtoL[Rnum] = Lnum;
        }
        else if (x == n - 1 and now[n - 2]) {
            Lnum = RtoL[n - 2];
            Rnum = n - 1;
            LtoR[Lnum] = Rnum;
            RtoL[Rnum] = Lnum;
        }
        else if ((x == 0 or x == n - 1) or (!now[x - 1] and !now[x + 1])) {
            Lnum = x;
            Rnum = x;
            LtoR[x] = x;
            RtoL[x] = x;
        }
        else if (now[x - 1] and now[x + 1]) {
            Lnum = RtoL[x - 1];
            Rnum = LtoR[x + 1];
            LtoR[Lnum] = Rnum;
            RtoL[Rnum] = Lnum;
        }
        else if (now[x - 1]) {
            Lnum = RtoL[x - 1];
            Rnum = x;
            LtoR[Lnum] = Rnum;
            RtoL[Rnum] = Lnum;
        }
        else {
            Lnum = x;
            Rnum = LtoR[x + 1];
            LtoR[Lnum] = Rnum;
            RtoL[Rnum] = Lnum;
        }
        ans = max(ans, (Rnum-Lnum+1) * RMax(Lnum, Rnum));
        now[x] = 1;
    }

    reverse(Ans.begin(), Ans.end());
    for (auto x : Ans) cout << x << "\n";

    return 0;
}