#include <bits/stdc++.h>
using namespace std;
long long inf = 1e9 + 7;
long long mod = 16714589;
long long gcd(long long a, long long b) { return (b ? gcd(b, a % b) : a); }
long long pow2(long long a, long long b) {
  if (b == 0) return 1;
  if (b % 2 == 1) {
    return a * pow2(a, b - 1);
  }
  if (b % 2 == 0) {
    long long c = pow2(a, b / 2);
    return c * c;
  }
}
vector<long long> st;
struct sptable {
  vector<vector<long long>> g, gi;
  vector<long long> maxst;
  sptable(vector<long long> a) {
    g.resize(a.size(), vector<long long>(29, -1));
    gi.resize(a.size(), vector<long long>(29, -1));
    maxst.resize(a.size() + 1);
    for (long long i = 0; i < a.size(); i++) {
      g[i][0] = a[i];
      gi[i][0] = i;
    }
    for (long long j = 1; j < 29; j++) {
      for (long long i = 0; i < a.size() && i + st[j] - 1 < a.size(); i++) {
        if (g[i][j - 1] > g[i + st[j - 1]][j - 1]) {
          gi[i][j] = gi[i][j - 1];
          g[i][j] = g[i][j - 1];
        } else {
          gi[i][j] = gi[i + st[j - 1]][j - 1];
          g[i][j] = g[i + st[j - 1]][j - 1];
        }
      }
    }
    long long k = 0;
    for (long long i = 1; i <= a.size(); i++) {
      if (i >= st[k + 1]) {
        k++;
      }
      if (i < st[k])
        maxst[i] = k - 1;
      else {
        maxst[i] = k;
      }
    }
  }
  long long getMax(long long l, long long r) {
    long long len = r - l + 1;
    long long res = 0;
    long long ma =
        max(g[l][maxst[len]], g[l + len % st[maxst[len]]][maxst[len]]);
    long long mai;
    if (g[l][maxst[len]] == ma)
      mai = gi[l][maxst[len]];
    else
      mai = gi[l + len % st[maxst[len]]][maxst[len]];
    res += ma * (long long)(mai - l + 1) * (long long)(r - mai + 1);
    if (l <= mai - 1) res += getMax(l, mai - 1);
    if (mai + 1 <= r) res += getMax(mai + 1, r);
    return res;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, q;
  cin >> n >> q;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<long long> b(n - 1);
  for (long long i = 0; i + 1 < n; i++) {
    b[i] = abs(a[i] - a[i + 1]);
  }
  st.resize(29);
  st[0] = 1;
  for (long long i = 1; i < 29; i++) {
    st[i] = st[i - 1] * 2;
  }
  sptable d(b);
  for (long long i = 0; i < q; i++) {
    long long l, r;
    cin >> l >> r;
    l--;
    r -= 2;
    cout << d.getMax(l, r) << endl;
  }
}

### Prompt

Develop a solution in CPP to the problem described below:

A function <image> is called Lipschitz continuous if there is a real constant K such that the inequality |f(x) - f(y)| ≤ K·|x - y| holds for all <image>. We'll deal with a more... discrete version of this term.

For an array <image>, we define it's Lipschitz constant <image> as follows:

  * if n < 2, <image>
  * if n ≥ 2, <image> over all 1 ≤ i < j ≤ n



In other words, <image> is the smallest non-negative integer such that |h[i] - h[j]| ≤ L·|i - j| holds for all 1 ≤ i, j ≤ n.

You are given an array <image> of size n and q queries of the form [l, r]. For each query, consider the subarray <image>; determine the sum of Lipschitz constants of all subarrays of <image>.

Input

The first line of the input contains two space-separated integers n and q (2 ≤ n ≤ 100 000 and 1 ≤ q ≤ 100) — the number of elements in array <image> and the number of queries respectively.

The second line contains n space-separated integers <image> (<image>).

The following q lines describe queries. The i-th of those lines contains two space-separated integers li and ri (1 ≤ li < ri ≤ n).

Output

Print the answers to all queries in the order in which they are given in the input. For the i-th query, print one line containing a single integer — the sum of Lipschitz constants of all subarrays of <image>.

Examples

Input

10 4
1 5 2 9 1 3 4 2 1 7
2 4
3 8
7 10
1 9


Output

17
82
23
210


Input

7 6
5 7 7 4 6 6 2
1 2
2 3
2 6
1 7
4 7
3 5


Output

2
0
22
59
16
8

Note

In the first query of the first sample, the Lipschitz constants of subarrays of <image> with length at least 2 are:

  * <image>
  * <image>
  * <image>



The answer to the query is their sum.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long inf = 1e9 + 7;
long long mod = 16714589;
long long gcd(long long a, long long b) { return (b ? gcd(b, a % b) : a); }
long long pow2(long long a, long long b) {
  if (b == 0) return 1;
  if (b % 2 == 1) {
    return a * pow2(a, b - 1);
  }
  if (b % 2 == 0) {
    long long c = pow2(a, b / 2);
    return c * c;
  }
}
vector<long long> st;
struct sptable {
  vector<vector<long long>> g, gi;
  vector<long long> maxst;
  sptable(vector<long long> a) {
    g.resize(a.size(), vector<long long>(29, -1));
    gi.resize(a.size(), vector<long long>(29, -1));
    maxst.resize(a.size() + 1);
    for (long long i = 0; i < a.size(); i++) {
      g[i][0] = a[i];
      gi[i][0] = i;
    }
    for (long long j = 1; j < 29; j++) {
      for (long long i = 0; i < a.size() && i + st[j] - 1 < a.size(); i++) {
        if (g[i][j - 1] > g[i + st[j - 1]][j - 1]) {
          gi[i][j] = gi[i][j - 1];
          g[i][j] = g[i][j - 1];
        } else {
          gi[i][j] = gi[i + st[j - 1]][j - 1];
          g[i][j] = g[i + st[j - 1]][j - 1];
        }
      }
    }
    long long k = 0;
    for (long long i = 1; i <= a.size(); i++) {
      if (i >= st[k + 1]) {
        k++;
      }
      if (i < st[k])
        maxst[i] = k - 1;
      else {
        maxst[i] = k;
      }
    }
  }
  long long getMax(long long l, long long r) {
    long long len = r - l + 1;
    long long res = 0;
    long long ma =
        max(g[l][maxst[len]], g[l + len % st[maxst[len]]][maxst[len]]);
    long long mai;
    if (g[l][maxst[len]] == ma)
      mai = gi[l][maxst[len]];
    else
      mai = gi[l + len % st[maxst[len]]][maxst[len]];
    res += ma * (long long)(mai - l + 1) * (long long)(r - mai + 1);
    if (l <= mai - 1) res += getMax(l, mai - 1);
    if (mai + 1 <= r) res += getMax(mai + 1, r);
    return res;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, q;
  cin >> n >> q;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<long long> b(n - 1);
  for (long long i = 0; i + 1 < n; i++) {
    b[i] = abs(a[i] - a[i + 1]);
  }
  st.resize(29);
  st[0] = 1;
  for (long long i = 1; i < 29; i++) {
    st[i] = st[i - 1] * 2;
  }
  sptable d(b);
  for (long long i = 0; i < q; i++) {
    long long l, r;
    cin >> l >> r;
    l--;
    r -= 2;
    cout << d.getMax(l, r) << endl;
  }
}

```