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 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≤i<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≤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.
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 "+jx". 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 "-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.
4 1
1 2 1 5
2
+ 3 2
- 4 1
4 1
1 2 3 4
0