#include <bits/stdc++.h>
const int maxn = 200000;
using namespace std;
int a[maxn], b[maxn];
int l[maxn], r[maxn];
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  a[0] = 0;
  for (int i = 1; i <= n; i++)
    scanf("%d", &a[i]), b[i - 1] = abs(a[i] - a[i - 1]);
  for (int i = 1; i <= q; i++) {
    int x, y;
    long long ans = 0;
    scanf("%d%d", &x, &y);
    y--;
    l[x] = x - 1;
    r[y] = y + 1;
    for (int j = x + 1; j <= y; j++) {
      l[j] = j - 1;
      while (l[j] >= x && b[l[j]] < b[j]) l[j] = l[l[j]];
    }
    for (int j = y - 1; j >= x; j--) {
      r[j] = j + 1;
      while (r[j] <= y && b[r[j]] <= b[j]) r[j] = r[r[j]];
    }
    for (int j = x; j <= y; j++)
      ans += (long long)(l[j] - j) * (j - r[j]) * b[j];
    printf("%I64d\n", ans);
  }
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

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>
const int maxn = 200000;
using namespace std;
int a[maxn], b[maxn];
int l[maxn], r[maxn];
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  a[0] = 0;
  for (int i = 1; i <= n; i++)
    scanf("%d", &a[i]), b[i - 1] = abs(a[i] - a[i - 1]);
  for (int i = 1; i <= q; i++) {
    int x, y;
    long long ans = 0;
    scanf("%d%d", &x, &y);
    y--;
    l[x] = x - 1;
    r[y] = y + 1;
    for (int j = x + 1; j <= y; j++) {
      l[j] = j - 1;
      while (l[j] >= x && b[l[j]] < b[j]) l[j] = l[l[j]];
    }
    for (int j = y - 1; j >= x; j--) {
      r[j] = j + 1;
      while (r[j] <= y && b[r[j]] <= b[j]) r[j] = r[r[j]];
    }
    for (int j = x; j <= y; j++)
      ans += (long long)(l[j] - j) * (j - r[j]) * b[j];
    printf("%I64d\n", ans);
  }
  return 0;
}

```