content: package codingquestions.leetcode;
  
  /**
   * 2601. Prime Subtraction Operation
   * Solved
   * Medium
   * Topics
   * Companies
   * Hint
   * You are given a 0-indexed integer array nums of length n.
   * <p>
   * You can perform the following operation as many times as you want:
   * <p>
   * Pick an index i that you haven’t picked before, and pick a prime p strictly less than nums[i], then subtract p from nums[i].
   * Return true if you can make nums a strictly increasing array using the above operation and false otherwise.
   * <p>
   * A strictly increasing array is an array whose each element is strictly greater than its preceding element.
   **/
  public class PrimeSubtractionOperation {
      private static final int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021};
  
      public boolean primeSubOperation(int[] nums) {
          int prev = 0;
          for (int num : nums) {
              if (num <= prev) {
                  return false;
              }
              int i = bisectLeft(primes, num - prev) - 1;
              if (i != -1) {
                  num -= primes[i];
              }
              prev = num;
          }
          return true;
      }
  
      private int bisectLeft(int[] arr, int target) {
          int left = 0;
          int right = arr.length;
          while (left < right) {
              int mid = (left + right) / 2;
              if (arr[mid] < target) {
                  left = mid + 1;
              } else {
                  right = mid;
              }
          }
          return left;
      }
  }
  