Expression

Given $n$ integers $x_1,x_2,...,x_n$. Arrange between them the signs "+" and "-" so that the value of the resulting expression is equal to $s$.

Input

The first line contains two values $n(2\le n\le 24)$ and $s(-10^9\le s\le 10^9)$. The next line contains $n$ integers $x_1,x_2,...,x_n(0\le x_i\le 5\cdot 10^7)$.

Output

If it is impossible to get the result, print "No solution". Otherwise print the equality. If the solution is not unique, print any.

Examples