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.