There are n piles of pebbles on the table, the i-th pile contains ai pebbles. Your task is to paint each pebble using one of the k given colors so that for each color c and any two piles i and j the difference between the number of pebbles of color c in pile i and number of pebbles of color c in pile j is at most one.
In other words, let's say that bi,c is the number of pebbles of color c in the i-th pile. Then for any 1≤c≤k, 1≤i,j≤n the following condition must be satisfied |bi,c-bj,c|≤1. It isn't necessary to use all k colors: if color c hasn't been used in pile i, then bi,c is considered to be zero.
Output
If there is no way to paint the pebbles satisfying the given condition, output "
NO" (without quotes) .
Otherwise in the first line output "
YES" (without quotes). Then
n lines should follow, the
i-th of them should contain
ai space-separated integers.
j-th (
1≤j≤ai) of these integers should be equal to the color of the
j-th pebble in the
i-th pile.
If there are several possible answers, you may output any of them.
Examples
Output
YES
1
1 4
1 2 4
1 2 3 4
Output
YES
1 2 3
1 3
1 2 3 4
1 3 4
1 1 2 3 4