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B. Trees in a Row

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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?

Input

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.

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 ≤ *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.

Examples

Input

4 1

1 2 1 5

Output

2

+ 3 2

- 4 1

Input

4 1

1 2 3 4

Output

0

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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