Search an element in a matrix

class Solution {
public:
  bool searchMatrix(vector<vector<int>> &matrix, int target) {
    int n = matrix.size();
    int m = matrix[0].size();
    int l = 0, r = n * m - 1;

    while (l <= r) {
      int mid = (l + r) / 2;
      int N = mid / m;
      int M = mid % m;

      if (target == matrix[N][M])
        return true;
      else if (target < matrix[N][M])
        r = mid - 1;
      else
        l = mid + 1;
    }

    return false;
  }
};