Farmer John wants to fairly split haybales between his two favorite cows Bessie and Elsie. He has $N$ ( $1\le N\le 2\cdot 10^5$) haybales sorted in non-increasing order, where the $i$-th haybale has $a_i$ units of hay ($2\cdot 10^5\ge a_1\ge a_2 \ge \dots \ge a_N \ge 1$).

Farmer John is considering splitting a contiguous range of haybales $a_l, \dots, a_r$ between Bessie and Elsie. He has decided to process the haybales in order from $l$ to $r$, and when processing the $i$-th haybale he will give it to the cow who currently has less hay (if it is a tie, he will give it to Bessie).

You are given $Q$ ($1\le Q\le 2\cdot 10^5$) queries, each with three integers $l,r,x$ ($1\le l\le r\le N$, $|x|\le 10^9$). For each query, output how many more units of hay Bessie will have than Elsie after processing haybales $l$ to $r$, if Bessie starts with $x$ more units than Elsie. Note that this value is negative if Elsie ends up with more haybales than Bessie.

SAMPLE INPUT:

2
3 1
15
1 1 -2
1 1 -1
1 1 0
1 1 1
1 1 2
1 2 -2
1 2 -1
1 2 0
1 2 1
1 2 2
2 2 -2
2 2 -1
2 2 0
2 2 1
2 2 2

SAMPLE OUTPUT:

1
2
3
-2
-1
0
1
2
-1
0
-1
0
1
0
1

For the 3rd query, Elsie and Bessie start with the same number of hay. After processing haybale $1$, Bessie will receive $3$ hay, and Bessie will have $3$ more hay than Elsie.

For the 9th query, Bessie starts with $1$ more hay than Elsie, then after processing the 1st haybale, has $2$ less hay than Elsie, and after processing the 2nd haybale, has $1$ less hay than Elsie.

SAMPLE INPUT:

5
4 4 3 1 1
7
1 1 20
1 2 20
1 5 20
1 1 0
1 5 0
1 4 0
3 5 2

SAMPLE OUTPUT:

16
12
7
4
1
2
1

In the 5th query, there are $5$ haybales to process. Bessie receives $4$ hay, then Elsie receives $4$ hay, then Bessie receives $3$ hay, then Elsie receives $1$ hay, then Elsie receives $1$ hay.

Problem credits: Benjamin Qi