The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Yandex.Algorithm 2011: Round 2 |
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Finished |

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data structures

implementation

math

two pointers

*2200

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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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