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.

The input file contains several test cases. 
Each test case starts with two numbers $n, k$. Input is terminated by $n=k=0$. Otherwise, $1 \leq n \leq 100,000$ and there follow n integers with absolute values $\leq 10,000$ which constitute the sequence. Then follow $k$ queries for this sequence. Each query is a target $t$ with $0 \leq t \leq 1,000,000,000$.

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 $n$.