Buying fruits

For $m$ rubles $n$ items of fruits was bought. It is known that one watermelon costs $a$ rubles, one apple costs $b$ rubles and one plum costs $c$ rubles.

Determine how many items of each fruit was purchased.

Input

The first line contains two positive integers $m$ and $n(1\le m,n\le 10^6)$. Second line contains $a,b,c(1\le a,b,c\le 10^6)$ — the prices of each fruit.

Output

Print in one line three natural numbers — the amount of each fruit. If there are multiple solutions, output where number of watermelons is minimum, and even if now there are multiple solutions, print where number of apples is minimum. If there are no solutions output "NO SOLUTION".

Examples