An array of positive integers a₁, a₂, ..., 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 ≤ 10⁶) — 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).

Note

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

$\text{[math]}$ Then K₁ = 3, K₂ = 2, K₃ = 1, so the power is equal to 3²·1 + 2²·2 + 1²·3 = 20.

Powerful array

Examples