Very simple problem

Input

The first line of the input provides two integers: $n$ and $m$ , representing the number of variables and the number of equations, respectively ( $1 \leq n \leq 600$ 1 \leq n \leq 600, $1 \leq m \leq 1000$ 1 \leq m \leq 1000). The following $m$ lines describe the equations, where the $i$ -th equation is given by real numbers $a_{i 1}, \dots, a_{in}$ a_{i1}, \ldots, a_{in} and $b_{i}$ b_i. The final line contains $n$ real numbers: $c_{1}, \dots, c_{n}$ c_1, \ldots, c_n. Each $a_{ij}$ a_{ij} does not exceed $1 0^{3}$ 10^3 in absolute value, and all $b_{i}$ b_i and $c_{i}$ c_i do not exceed $1 0^{9}$ 10^9 in absolute value.

Output

If there are no feasible solutions to the problem, output No solution. If the objective function can achieve an infinitely large value, output Unbounded.

Otherwise, first output the word Bounded. On the second line, provide the values of the variables that maximize the objective function. Your solution will be considered correct if the value of the objective function at your solution differs from the correct value by no more than $1 0^{- 6}$ 10^{-6} in absolute or relative error.

Examples

Example 1

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