class Solution {
 public:
  int minPatches(vector<int>& nums, int n) {
    int ans = 0;
    int i = 0;      // point to nums
    long miss = 1;  // min sum in [1, n] we might miss

    while (miss <= n)
      if (i < nums.size() && nums[i] <= miss) {
        miss += nums[i++];
      } else {
        // greedily add miss itself to increase the range
        // from [1, miss) to [1, 2 * miss)
        miss += miss;
        ++ans;
      }

    return ans;
  }
};

class Solution {
  public int minPatches(int[] nums, int n) {
    int ans = 0;
    int i = 0;     // point to nums
    long miss = 1; // min sum in [1, n] we might miss

    while (miss <= n)
      if (i < nums.length && nums[i] <= miss) {
        miss += nums[i++];
      } else {
        // greedily add miss itself to increase the range
        // from [1, miss) to [1, 2 * miss)
        miss += miss;
        ++ans;
      }

    return ans;
  }
}

class Solution:
  def minPatches(self, nums: List[int], n: int) -> int:
    ans = 0
    i = 0     # point to nums
    miss = 1  # min sum in [1, n] we might miss

    while miss <= n:
      if i < len(nums) and nums[i] <= miss:
        miss += nums[i]
        i += 1
      else:
        # greedily add miss itself to increase the range
        # from [1, miss) to [1, 2 * miss)
        miss += miss
        ans += 1

    return ans