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?

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 ≤ 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
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, k, mn, cnt = 0, start, top;
  cin >> n >> k;
  int a[n + 1], b[n + 1];
  a[0] = 0;
  b[0] = 0;
  mn = 1001;
  for (int i = 1; i <= n; i++) cin >> a[i], b[i] = a[i];
  for (int i = 1; i <= 1000; i++) {
    for (int l = 1; l <= n; l++) b[l] = a[l];
    if (b[1] == i)
      cnt = 0;
    else
      cnt = 1, b[1] = i;
    for (int j = 1; j < n; j++) {
      if (b[j + 1] - b[j] != k) {
        cnt++;
        b[j + 1] = b[j] + k;
      }
    }
    if (cnt < mn) {
      mn = cnt;
      start = i;
    }
  }
  cout << mn << endl;
  if (start != a[1]) {
    if (start > a[1])
      cout << "+ "
           << "1 " << start - a[1] << endl;
    else
      cout << "- "
           << "1 " << a[1] - start << endl;
  }
  a[1] = start;
  for (int j = 1; j < n; j++) {
    if (a[j + 1] - a[j] != k) {
      top = a[j] + k;
      if (top > a[j + 1])
        cout << "+ " << j + 1 << " " << top - a[j + 1] << endl;
      else
        cout << "- " << j + 1 << " " << a[j + 1] - top << endl;
      a[j + 1] = top;
    }
  }
  return 0;
}
