A9440 | Trees in a Row

The Queen of England has $n$ trees growing in a row in her garden. At that, the $i$ -th $(1<=i<=n)$ tree from the left has height $a_{i}$ meters. Today the Queen decided to update the scenery of her garden. She wants the trees' heights to meet the condition: for all $i$ $(1<=i<n)$ , $a_{i+1}-a_{i}=k$ , where $k$ is the number the Queen chose.

Unfortunately, the royal gardener is not a machine and he cannot fulfill the desire of the Queen instantly! In one minute, the gardener can either decrease the height of a tree to any positive integer height or increase the height of a tree to any positive integer height. How should the royal gardener act to fulfill a whim of Her Majesty in the minimum number of minutes?

The first line contains two space-separated integers: $n$ , $k$ ( $1<=n,k<=1000)$ . The second line contains $n$ space-separated integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=1000$ ) — the heights of the trees in the row.

In the first line print a single integer $p$ — the minimum number of minutes the gardener needs. In the next $p$ lines print the description of his actions.

If the gardener needs to increase the height of the $j$ -th ( $1<=j<=n$ ) tree from the left by $x$ $(x>=1)$ meters, then print in the corresponding line "+ j x". If the gardener needs to decrease the height of the $j$ -th ( $1<=j<=n$ ) tree from the left by $x$ $(x>=1)$ meters, print on the corresponding line "- j x".

If there are multiple ways to make a row of trees beautiful in the minimum number of actions, you are allowed to print any of them.