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 MAXN = 1e6 + 5, off = 1 << 20;
struct TournamentMax {
  pair<int, int> t[2 * off];
  TournamentMax() { memset(t, 0, sizeof(t)); }
  void update(int x, int val) {
    t[x + off] = pair<int, int>(val, x);
    x += off;
    for (x /= 2; x > 0; x /= 2) t[x] = max(t[x * 2], t[x * 2 + 1]);
  }
  void build() {
    for (int i = off - 1; i > 0; --i) t[i] = max(t[i * 2], t[i * 2 + 1]);
  }
  pair<int, int> get(int x, int lo, int hi, int a, int b) {
    if (lo >= b || hi <= a) return pair<int, int>(0, 0);
    if (lo >= a && hi <= b) return t[x];
    int mid = (lo + hi) >> 1;
    return max(get(x * 2, lo, mid, a, b), get(x * 2 + 1, mid, hi, a, b));
  }
} Tmax;
struct TournamentSum {
  long long t[2 * off], p[2 * off];
  TournamentSum() { reset(); }
  void reset() {
    for (int i = 0; i < 2 * off; ++i) t[i] = p[i] = 0;
  }
  void prop(int x, int lo, int hi) {
    if (p[x] == 0) return;
    t[x] += (hi - lo) * p[x];
    if (x < off) {
      p[x * 2] += p[x];
      p[x * 2 + 1] += p[x];
    }
    p[x] = 0;
  }
  void update(int x, int lo, int hi, int a, int b, int val) {
    prop(x, lo, hi);
    if (lo >= b || hi <= a) return;
    if (lo >= a && hi <= b) {
      p[x] += val;
      prop(x, lo, hi);
      return;
    }
    int mid = (lo + hi) >> 1;
    update(x * 2, lo, mid, a, b, val);
    update(x * 2 + 1, mid, hi, a, b, val);
    t[x] = t[x * 2] + t[x * 2 + 1];
  }
  long long get(int x, int lo, int hi, int a, int b) {
    prop(x, lo, hi);
    if (lo >= b || hi <= a) return 0;
    if (lo >= a && hi <= b) return t[x];
    int mid = (lo + hi) >> 1;
    return get(x * 2, lo, mid, a, b) + get(x * 2 + 1, mid, hi, a, b);
  }
} Tsum;
int n, q, ar[MAXN], l[MAXN], r[MAXN];
vector<pair<int, int> > lt[MAXN], rt[MAXN];
long long sol[MAXN];
void razdvoji(int lo, int hi) {
  if (lo > hi) return;
  int pos = Tmax.get(1, 0, off, lo, hi + 1).second;
  l[pos] = lo;
  r[pos] = hi;
  razdvoji(lo, pos - 1);
  razdvoji(pos + 1, hi);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> q;
  for (int i = 0; i < n; ++i) {
    cin >> ar[i];
    Tmax.t[i + off] = pair<int, int>(ar[i], i);
  }
  Tmax.build();
  for (int i = 0; i < q; ++i) cin >> l[i];
  for (int i = 0; i < q; ++i) cin >> r[i];
  for (int i = 0; i < q; ++i) {
    sol[i] += (r[i] - l[i] + 1);
    l[i]--;
    r[i]--;
    lt[l[i]].push_back(pair<int, int>(r[i], i));
    rt[r[i]].push_back(pair<int, int>(l[i], i));
  }
  razdvoji(0, n - 1);
  for (int i = 0; i < n; ++i) {
    Tsum.update(1, 0, off, l[i], i, 1);
    for (auto it : rt[i])
      sol[it.second] += Tsum.get(1, 0, off, it.first, i + 1);
  }
  Tsum.reset();
  for (int i = n - 1; i >= 0; --i) {
    Tsum.update(1, 0, off, i, r[i], 1);
    for (auto it : lt[i]) sol[it.second] += Tsum.get(1, 0, off, i, it.first);
  }
  for (int i = 0; i < q; ++i) cout << sol[i] << " ";
}