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?

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.