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D. Powerful array

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAn array of positive integers *a* _{1}, *a* _{2}, ..., *a* _{ n} is given. Let us consider its arbitrary subarray *a* _{ l}, *a* _{ l + 1}..., *a* _{ r}, where 1 ≤ *l* ≤ *r* ≤ *n*. For every positive integer *s* denote by *K* _{ s} the number of occurrences of *s* into the subarray. We call the power of the subarray the sum of products *K* _{ s}·*K* _{ s}·*s* for every positive integer *s*. The sum contains only finite number of nonzero summands as the number of different values in the array is indeed finite.

You should calculate the power of *t* given subarrays.

Input

First line contains two integers *n* and *t* (1 ≤ *n*, *t* ≤ 200000) — the array length and the number of queries correspondingly.

Second line contains *n* positive integers *a* _{ i} (1 ≤ *a* _{ i} ≤ 10^{6}) — the elements of the array.

Next *t* lines contain two positive integers *l*, *r* (1 ≤ *l* ≤ *r* ≤ *n*) each — the indices of the left and the right ends of the corresponding subarray.

Output

Output *t* lines, the *i*-th line of the output should contain single positive integer — the power of the *i*-th query subarray.

Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preferred to use cout stream (also you may use %I64d).

Examples

Input

3 2

1 2 1

1 2

1 3

Output

3

6

Input

8 3

1 1 2 2 1 3 1 1

2 7

1 6

2 7

Output

20

20

20

Note

Consider the following array (see the second sample) and its [2, 7] subarray (elements of the subarray are colored):

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