Problem3121--Trees in a Row

3121: Trees in a Row

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The Queen of England has n trees growing in a row in her garden. At that, the i-th (1≤in) 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?

Input

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.

Output

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≤jn) 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≤jn) 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.

Examples
Input
4 1
1 2 1 5
Output
2
+ 3 2
- 4 1
Input
4 1
1 2 3 4
Output
0

Source/Category