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?

输入描述:

The first line contains two space-separated integers: n, k (1 ≤ n, k ≤ 1000). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the heights of the trees in the row.

输出描述:

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.