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F. Xors on Segments
time limit per test
10 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given an array with n integers ai and m queries. Each query is described by two integers (lj, rj).

Let's define the function . The function is defined for only u ≤ v.

For each query print the maximal value of the function f(ax, ay) over all lj ≤ x, y ≤ rj,  ax ≤ ay.

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 ai (1 ≤ ai ≤ 106) — the elements of the array a.

Each of the next m lines contains two integers lj, rj (1 ≤ lj ≤ rj ≤ n) – the parameters of the j-th query.

Output

For each query print the value aj on a separate line — the maximal value of the function f(ax, ay) over all lj ≤ x, y ≤ rj,  ax ≤ ay.

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
1
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
10
21313
21313
21313
21313
21313
21312
21313
21313
21313
21313
2314
2315
2315
214
215
323
1
323
322