Problem: You are given a permutation p_1, p_2, ..., p_n. You should answer q queries. Each query is a pair (l_i, r_i), and you should calculate f(l_i, r_i).

Let's denote m_{l, r} as the position of the maximum in subsegment p_l, p_{l+1}, ..., p_r.

Then f(l, r) = (r - l + 1) + f(l, m_{l,r} - 1) + f(m_{l,r} + 1, r) if l ≤ r or 0 otherwise.

Input

The first line contains two integers n and q (1 ≤ n ≤ 10^6, 1 ≤ q ≤ 10^6) — the size of the permutation p and the number of queries.

The second line contains n pairwise distinct integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n, p_i ≠ p_j for i ≠ j) — permutation p.

The third line contains q integers l_1, l_2, ..., l_q — the first parts of the queries.

The fourth line contains q integers r_1, r_2, ..., r_q — the second parts of the queries.

It's guaranteed that 1 ≤ l_i ≤ r_i ≤ n for all queries.

Output

Print q integers — the values f(l_i, r_i) for the corresponding queries.

Example

Input


4 5
3 1 4 2
2 1 1 2 1
2 3 4 4 1


Output


1 6 8 5 1 

Note

Description of the queries: 

  1. f(2, 2) = (2 - 2 + 1) + f(2, 1) + f(3, 2) = 1 + 0 + 0 = 1; 
  2. f(1, 3) = (3 - 1 + 1) + f(1, 2) + f(4, 3) = 3 + (2 - 1 + 1) + f(1, 0) + f(2, 2) = 3 + 2 + (2 - 2 + 1) = 6; 
  3. f(1, 4) = (4 - 1 + 1) + f(1, 2) + f(4, 4) = 4 + 3 + 1 = 8; 
  4. f(2, 4) = (4 - 2 + 1) + f(2, 2) + f(4, 4) = 3 + 1 + 1 = 5; 
  5. f(1, 1) = (1 - 1 + 1) + 0 + 0 = 1. 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 10;
long long c[N], ANS, pans, t[N];
int n, a[N], m, R[N], L[N];
int seg[N << 2];
inline void pushup(int rt) { seg[rt] = min(seg[rt << 1], seg[rt << 1 | 1]); }
void ini(int k) {
  int i;
  for (i = 1; i <= 4 * n; ++i) seg[i] = k;
}
inline void motify(int rt, int l, int r, int k, int d) {
  if (l == r) {
    seg[rt] = d;
    return;
  }
  int mid = l + r >> 1;
  if (mid >= k)
    motify(rt << 1, l, mid, k, d);
  else
    motify(rt << 1 | 1, mid + 1, r, k, d);
  pushup(rt);
}
inline int query(int rt, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return seg[rt];
  int res = 1 << 30, mid = l + r >> 1;
  if (mid >= ql) res = min(res, query(rt << 1, l, mid, ql, qr));
  if (mid + 1 <= qr) res = min(res, query(rt << 1 | 1, mid + 1, r, ql, qr));
  return res;
}
long long sum[N << 2], tag[N << 2];
void pd(int rt, int len) {
  if (tag[rt]) {
    tag[rt << 1] += tag[rt];
    tag[rt << 1 | 1] += tag[rt];
    sum[rt << 1] += (long long)(len - len / 2) * tag[rt];
    sum[rt << 1 | 1] += tag[rt] * (long long)(len >> 1);
    tag[rt] = 0;
  }
}
void pu(int rt) { sum[rt] = sum[rt << 1] + sum[rt << 1 | 1]; }
void motify(int rt, int l, int r, int ql, int qr, long long k) {
  if (ql <= l && r <= qr) {
    sum[rt] += k * (long long)(r - l + 1);
    tag[rt] += k;
    return;
  }
  pd(rt, r - l + 1);
  int mid = l + r >> 1;
  if (mid >= ql) motify(rt << 1, l, mid, ql, qr, k);
  if (mid + 1 <= qr) motify(rt << 1 | 1, mid + 1, r, ql, qr, k);
  pu(rt);
}
long long que(int rt, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return sum[rt];
  pd(rt, r - l + 1);
  int mid = l + r >> 1;
  long long res = 0;
  if (mid >= ql) res += que(rt << 1, l, mid, ql, qr);
  if (mid + 1 <= qr) res += que(rt << 1 | 1, mid + 1, r, ql, qr);
  pu(rt);
  return res;
}
vector<pair<int, int> > q1[N], q2[N];
long long ans[N];
int qll[N], qrr[N];
int main() {
  scanf("%d%d", &n, &m);
  register int i, j;
  for (i = 1; i <= n; ++i) scanf("%d", &a[i]);
  ini(n + 1);
  for (i = n; i >= 1; --i) {
    if (a[i] == n)
      R[i] = n + 1;
    else {
      R[i] = query(1, 1, n, a[i] + 1, n);
    }
    motify(1, 1, n, a[i], i);
  }
  ini(0);
  for (i = 1; i <= n; ++i) {
    if (a[i] == n)
      L[i] = 0;
    else {
      L[i] = -query(1, 1, n, a[i] + 1, n);
    }
    motify(1, 1, n, a[i], -i);
  }
  for (i = 1; i <= m; ++i) scanf("%d", &qll[i]);
  for (i = 1; i <= m; ++i) scanf("%d", &qrr[i]);
  for (i = 1; i <= m; ++i) {
    q1[qll[i]].push_back(make_pair(qrr[i], i));
    q2[qrr[i]].push_back(make_pair(qll[i], i));
  }
  for (i = n; i >= 1; --i) {
    if (i + 1 <= R[i] - 1) motify(1, 1, n, i + 1, R[i] - 1, 1);
    vector<pair<int, int> >::iterator it;
    for (it = q1[i].begin(); it != q1[i].end(); ++it) {
      ans[(*it).second] += que(1, 1, n, i, (*it).first);
    }
  }
  memset(sum, 0, sizeof(sum));
  memset(tag, 0, sizeof(tag));
  for (i = 1; i <= n; ++i) {
    if (L[i] + 1 <= i) motify(1, 1, n, L[i] + 1, i, 1);
    vector<pair<int, int> >::iterator it;
    for (it = q2[i].begin(); it != q2[i].end(); ++it) {
      ans[(*it).second] += que(1, 1, n, (*it).first, i);
    }
  }
  for (i = 1; i <= m; ++i) printf("%I64d ", ans[i]);
}