YSACODE discuss3

You are given an array with n integers a_i and m queries. Each query is described by two integers (l_j,r_j).

Let's define the function $\text{[math]}$ . The function is defined for only u≤v.

For each query print the maximal value of the function f(a_x,a_y) over all l_j≤x,y≤r_j, a_x≤a_y.

Input

The first line contains two integers n,m (1≤n≤5·10⁴, 1≤m≤5·10³) − the size of the array and the number of the queries.

The second line contains n integers a_i (1≤a_i≤10⁶) − the elements of the array a.

Each of the next m lines contains two integers l_j,r_j (1≤l_j≤r_j≤n) — the parameters of the j-th query.

Output

For each query print the value a_j on a separate line − the maximal value of the function f(a_x,a_y) over all l_j≤x,y≤r_j, a_x≤a_y.

Examples

Input

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

Output

7
7
7

Input

1 1
1
1 1

Output

Input

6 20
10 21312 2314 214 1 322
1 1
1 2
1 3
1 4
1 5
1 6
2 2
2 3
2 4
2 5
2 6
3 4
3 5
3 6
4 4
4 5
4 6
5 5
5 6
6 6

Output