The Queen of England has n trees growing in a row in her garden. At that, the i-th (1 \le i \le n) tree from the left has height ai 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 \le i \lt n), ai+1-ai=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 \le n,k \le 1000). The second line contains n space-separated integers a1,a2,...,an (1 \le ai \le 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 \le j \le n) tree from the left by x (x \ge 1) meters, then print in the corresponding line "+jx". If the gardener needs to decrease the height of the j-th (1 \le j \le n) tree from the left by x (x \ge 1) meters, print on the corresponding line "-jx".

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.