# 1418. Bound Found

Signals of most probably extra-terrestrial origin have been received and digitalized by The Aeronautic and Space Administration (that must be going through a defiant phase: “But I want to use feet, not meters!”). Each signal seems to come in two parts: a sequence of n integer values and a non-negative integer t. We’ll not go into details, but researchers found out that a signal encodes two integer values. These can be found as the lower and upper bound of a subrange of the sequence whose absolute value of its sum is closest to $t$.

You are given the sequence of $n$ integers and the non-negative target $t$. You are to find a non-empty range of the sequence (i.e. a continuous subsequence) and output its lower index $l$ and its upper index $u$. The absolute value of the sum of the values of the sequence from the $l$-th to the $u$-th element (inclusive) must be at least as close to $t$ as the absolute value of the sum of any other non-empty range.

### 输入格式

The input file contains several test cases.

Each test case starts with two numbers $n$ and $k$. Input is terminated by $n=k=0$. Otherwise, $1 \leq n \leq 100~000,1 \leq k \leq 250$ and there follow $n$ integers with absolute values no greater than $10000$ which constitute the sequence. Then follow $k$ queries for this sequence. Each query is a target $t$ with $0 \leq t \leq 10^9$.

### 输出格式

For each query output $3$ numbers on a line: some closest absolute sum and the lower and upper indices of some range where this absolute sum is achieved. Possible indices start with $1$ and go up to $n$.

### 样例

Input
5 1
-10 -5 0 5 10
3
10 2
-9 8 -7 6 -5 4 -3 2 -1 0
5 11
15 2
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
15 100
0 0

Output
5 4 4
5 2 8
9 1 1
15 1 15
15 1 15


4 人解决，4 人已尝试。

5 份提交通过，共有 7 份提交。

6.5 EMB 奖励。