A sequence s_1,s_2,\ldots,s_k can be approximated as a constant sequence c_1,c_2,\ldots,c_k where c_1=c_2=\cdots=c_k. The error of such an approximation is \frac{1}{k} \sum_{i=1}^k (s_i-c_i)^2.

You are given a sequence x_1,x_2,\ldots,x_n and q queries. For each query, your task is to approximate a consecutive subsequence of x using a constant sequence so that the error is as small as possible.

Input

The first input line contains two integers n and q: the length of the sequence and the number of queries.

The second input line contains n integers x_1,x_2,\ldots,x_n that describe the sequence.

Finally, the input contains q lines that describe the queries. Each line contains two integers a and b (1 \le a \le b \le n) that correspond to the subsequence x_a,x_{a+1},\ldots,x_b.

Output

For each query, output the smallest possible error (rounded to exactly 6 decimal digits) when the subsequence is approximated using a constant sequence.

Constraints

• 1 \le n,q \le 10^5
• 1 \le x_i \le 100

Example

Input:

8 3
1 2 3 3 3 3 3 1
2 3
4 6
1 8

Output:

0.250000
0.000000
0.734375

Explanation: The first query is a = 2 and b = 3 which refers to the subsequence (x_2, x_3) = (2,3). The best constant approximation of this sequence is (2.5, 2.5), and the error of this approximation is (0.5^2 + 0.5^2)/2 = 0.25.