Problem2196--Lipshitz Sequence

2196: Lipshitz Sequence

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
[Submit] [Status] [Web Board] [Creator:]

Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

A function 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 . We'll deal with a more... discrete version of this term.

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

  • if n<2,
  • if n≥2, over all 1≤i<jn

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

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

Input

The first line of the input contains two space-separated integers n and q (2≤n≤100000 and 1≤q≤100)− the number of elements in array and the number of queries respectively.

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

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

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 .

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 with length at least 2 are:

The answer to the query is their sum.

Source/Category