#include <bits/stdc++.h>
using namespace std;
struct node {
  int num, delta;
};
stack<node> Q;
int N, qus;
int data[100005] = {0};
long long int sum, ans;
void Q_Push(int num, int delta) {
  while (Q.top().delta <= delta) {
    long long int a = Q.top().delta, b = Q.top().num;
    Q.pop();
    sum -= a * (b - Q.top().num);
  }
  long long int a = Q.top().num;
  Q.push((node){num, delta});
  sum += delta * (num - a);
}
int main() {
  scanf("%d %d", &N, &qus);
  for (int i = 1; i <= N; i++) scanf("%d", &data[i]);
  while (qus--) {
    sum = ans = 0;
    int L, R;
    scanf("%d %d", &L, &R);
    Q.push((node){L, 0x7fffffff});
    for (int i = L + 1; i <= R; i++) {
      Q_Push(i, abs(data[i] - data[i - 1]));
      ans += sum;
    }
    printf("%lld\n", ans);
  }
  return 0;
}

### 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;
struct node {
  int num, delta;
};
stack<node> Q;
int N, qus;
int data[100005] = {0};
long long int sum, ans;
void Q_Push(int num, int delta) {
  while (Q.top().delta <= delta) {
    long long int a = Q.top().delta, b = Q.top().num;
    Q.pop();
    sum -= a * (b - Q.top().num);
  }
  long long int a = Q.top().num;
  Q.push((node){num, delta});
  sum += delta * (num - a);
}
int main() {
  scanf("%d %d", &N, &qus);
  for (int i = 1; i <= N; i++) scanf("%d", &data[i]);
  while (qus--) {
    sum = ans = 0;
    int L, R;
    scanf("%d %d", &L, &R);
    Q.push((node){L, 0x7fffffff});
    for (int i = L + 1; i <= R; i++) {
      Q_Push(i, abs(data[i] - data[i - 1]));
      ans += sum;
    }
    printf("%lld\n", ans);
  }
  return 0;
}

```