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>
struct Cuts {
  long long t[1000];
  int nonZero;
  Cuts() : nonZero(0) { memset(t, 0, sizeof(long long) * 1000); }
  void recountNonZero() {
    nonZero = 0;
    for (int i = 0; i < 1000; i++)
      if (t[i] != 0) nonZero++;
  }
  void subAll(int range, long long val) {
    for (int i = 0; i < range; i++) t[i] -= val;
    recountNonZero();
  }
  void print() const {
    std::cout << nonZero << std::endl;
    for (int i = 0; i < 1000; i++)
      if (t[i] != 0)
        std::cout << (t[i] > 0 ? "+ " : "- ") << (i + 1) << " "
                  << std::abs(t[i]) << std::endl;
  }
  long long& operator[](const int index) { return t[index]; }
};
struct Height {
  long long t[1000];
  Height() { memset(t, 0, sizeof(long long) * 1000); }
  long long& operator[](const int i) { return t[i]; }
};
int main() {
  int trees;
  long long K;
  Cuts minCuts;
  Height h, tmpH;
  std::ios_base::sync_with_stdio(false);
  std::cin >> trees >> K;
  for (int i = 0; i < trees; i++) std::cin >> h[i];
  tmpH = h;
  std::set<long long> uniqueCuts;
  minCuts[0] = 1 - tmpH[0];
  tmpH[0] = 1;
  uniqueCuts.insert(minCuts[0]);
  for (int i = 1; i < trees; i++) {
    minCuts[i] = tmpH[i - 1] + K - tmpH[i];
    tmpH[i] += minCuts[i];
    uniqueCuts.insert(minCuts[i]);
  }
  minCuts.recountNonZero();
  std::set<long long>::iterator it = uniqueCuts.begin(), end = uniqueCuts.end();
  while (it != end) {
    Cuts cuts = minCuts;
    cuts.subAll(trees, *it);
    if (cuts.nonZero < minCuts.nonZero) {
      bool valid = true;
      for (int i = 0; i < trees; i++)
        if (h[i] + cuts[i] <= 0) {
          valid = false;
          break;
        }
      if (valid) minCuts = cuts;
    }
    ++it;
  }
  for (int i = 1; i <= 1000; i++) {
    Cuts cuts = minCuts;
    cuts.subAll(trees, i);
    if (cuts.nonZero < minCuts.nonZero) {
      bool valid = true;
      for (int i = 0; i < trees; i++)
        if (h[i] + cuts[i] <= 0) {
          valid = false;
          break;
        }
      if (valid) minCuts = cuts;
    }
  }
  minCuts.print();
  return 0;
}
