Sameen has:

1. An array having N integers,
2. Q friends.

His friends are curious about the array. So, each of his friends asks Sameen a question about the array. Every question is described by 3 integers: i, j and k. In reply to a question, Sameen has to say the “k alternating sum” of the subarray starting at position i and ending at position j [1 based indexing].

“k alternating sum” of a subarray starting at position i and ending at position j can be calculated in the following way:

Add the first k numbers [starting from position i]

Subtract the second k numbers [starting from position i+k]

Add the third k numbers [starting from position i+2*k]

Subtract the fourth k numbers [starting from position i+3*k]

And so on till adding/subtracting the j-th number…

(j-i+1) will be divisible by k.

[See sample Input/output and explanation section for more details]

Can you help Sameen in answering the questions?

Input

The first line of input contains two integers N and Q. The next line contains N integers, the numbers in the array. Then each of the following Q lines contains 3 integers i, j & k.

Output

For each query output an integer in a separate line, the answer for that query. Queries should be answered in the order given in the input.

Constraints:

1 ≤ k ≤ 100000

1 ≤ N ≤ 100000

1 ≤ Q ≤ 100000

-1000000000 ≤ Value of a number in the array ≤ 1000000000

(j-i+1) will be divisible by k.

Example

Input:
6 6
4 1 -2 -3 4 5
2 5 2
1 6 1
1 6 3
1 6 6
3 3 1
3 4 1
Output:
-2
3
-3
9
-2
1

</p>

Explanation

In the first query, the subarray is [ 1, -2, -3, 4].

So “2 alternating sum” is equal to: [1-2]-[-3+4] = -2

For the second query, we get [4]-[1]+[-2]-[-3]+[4]-[5] = 3

N.B: Dataset is huge. Use faster I/O method.