description: Monocarp is playing yet another computer game. In this game, his character has to kill a dragon. The battle with the dragon lasts 100^{500} seconds, during which Monocarp attacks the dragon with a poisoned dagger. The i-th attack is performed at the beginning of the a_i-th second from the battle start. The dagger itself does not deal damage, but it applies a poison effect on the dragon, which deals 1 damage during each of the next k seconds (starting with the same second when the dragon was stabbed by the dagger). However, if the dragon has already been poisoned, then the dagger updates the poison effect (i.e. cancels the current poison effect and applies a new one).
  
  For example, suppose k = 4, and Monocarp stabs the dragon during the seconds 2, 4 and 10. Then the poison effect is applied at the start of the 2-nd second and deals 1 damage during the 2-nd and 3-rd seconds; then, at the beginning of the 4-th second, the poison effect is reapplied, so it deals exactly 1 damage during the seconds 4, 5, 6 and 7; then, during the 10-th second, the poison effect is applied again, and it deals 1 damage during the seconds 10, 11, 12 and 13. In total, the dragon receives 10 damage.
  
  Monocarp knows that the dragon has h hit points, and if he deals at least h damage to the dragon during the battle — he slays the dragon. Monocarp has not decided on the strength of the poison he will use during the battle, so he wants to find the minimum possible value of k (the number of seconds the poison effect lasts) that is enough to deal at least h damage to the dragon.
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.
  
  The first line of the test case contains two integers n and h (1 ≤ n ≤ 100; 1 ≤ h ≤ 10^{18}) — the number of Monocarp's attacks and the amount of damage that needs to be dealt.
  
  The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9; a_i < a_{i + 1}), where a_i is the second when the i-th attack is performed.
  
  Output
  
  For each test case, print a single integer — the minimum value of the parameter k, such that Monocarp will cause at least h damage to the dragon.
  
  Example
  
  Input
  
  
  4
  2 5
  1 5
  3 10
  2 4 10
  5 3
  1 2 4 5 7
  4 1000
  3 25 64 1337
  
  
  Output
  
  
  3
  4
  1
  470
  
  Note
  
  In the first example, for k=3, damage is dealt in seconds [1, 2, 3, 5, 6, 7].
  
  In the second example, for k=4, damage is dealt in seconds [2, 3, 4, 5, 6, 7, 10, 11, 12, 13].
  
  In the third example, for k=1, damage is dealt in seconds [1, 2, 4, 5, 7].
solution: import java.io.IOException;
  import java.io.InputStream;
  import java.io.PrintWriter; // System.out is a PrintStream
  import java.util.InputMismatchException;
  import java.util.Random;
  import java.util.Arrays;
  
  
  public class C {
      private static int MOD = (int)1e9 + 7, mod = 99_82_44_353;
      private static double PI = 3.14159265358979323846;
  
      public static void main(String[] args) throws IOException {
          FasterScanner scn = new FasterScanner();
          PrintWriter out = new PrintWriter(System.out);
          for (int tc = scn.nextInt(); tc > 0; tc--) {
              int N = scn.nextInt();
              long hp = scn.nextLong();
              int[] arr = new int[N];
              for (int i = 0; i < N; i++) {
                  arr[i] = scn.nextInt();
              }
              ruffleSort(arr);
              long lb = 1, ub = hp;
              while (lb < ub) {
                  long mid = ((ub - lb) >> 1) + lb;
                  long dmg = countDmg(arr, N, mid);
                  if (dmg < hp) {
                      lb = mid + 1;
                  } else {
                      ub = mid;
                  }
              }
              out.println(lb);
          }
          out.close();
      }
  
      private static long countDmg(int[] arr, int N, long dmg) {
          long ed = 0, ans = 0;
          for (int i = 0; i < N; i++) {
              if (ed >= arr[i]) {
                  ans -= dmg;
                  ans += arr[i] - arr[i - 1];
              }
              ans += dmg;
              ed = arr[i] + dmg - 1;
          }
          return ans;
      }
  
      /* ------------------- Sorting ------------------- */
      private static void ruffleSort(int[] arr) {
          int N = arr.length;
          Random rand = new Random();
          for (int i = 0; i < N; i++) {
              int oi = rand.nextInt(N), temp = arr[i];
              arr[i] = arr[oi];
              arr[oi] = temp;
          }
          Arrays.sort(arr);
      }
          
      /* ------------------- Sorting ------------------- */
      
      private static boolean isPalindrome(String str) {
          for (int i = 0, j = str.length() - 1; i < j; i++, j--) {
              if (str.charAt(i) != str.charAt(j)) {
                  return false;
              }
          }
          return true;
      }
      
      private static boolean isPalindrome(char[] str) {
          for (int i = 0, j = str.length - 1; i < j; i++, j--) {
              if (str[i] != str[j]) {
                  return false;
              }
          }
          return true;
      }
      
      /* ------------------- Pair class ------------------- */
      private static class Pair implements Comparable<Pair> {
  		int x, y;
  		Pair(int x, int y) {
  			this.x = x;
  			this.y = y;
  		}
  		public int compareTo(Pair o) {
  			return this.x == o.x ? this.y - o.y : this.x - o.x;
  		}
  	}
  
      /* ------------------- HCF and LCM ------------------- */
      private static int gcd(int num1, int num2) {
          int temp = 0;
          while (num2 != 0) {
              temp = num1;
              num1 = num2;
              num2 = temp % num2;
          }
          return num1;
      }
      
      private static int lcm(int num1, int num2) {
          return (int)((1L * num1 * num2) / gcd(num1, num2));
      }
      
      /* ------------------- primes and prime factorization ------------------- */
      private static boolean[] seive(int N) {
          // true means not prime, false means is a prime number :)
          boolean[] notPrimes = new boolean[N + 1];
          notPrimes[0] = notPrimes[1] = true;
          for (int i = 2; i * i <= N; i++) {
              if (notPrimes[i]) continue;
              for (int j = i * i; j <= N; j += i) {
                  notPrimes[j] = true;
              }
          }
          return notPrimes;
      }
  
  	/*
      private static TreeMap<Integer, Integer> primeFactors(long N) {
  		TreeMap<Integer, Integer> primeFact = new TreeMap<>();
  		for (int i = 2; i <= Math.sqrt(N); i++) {
              int count = 0;
              while (N % i == 0) {
                  N /= i;
                  count++;
              }
              if (count != 0) {
                  primeFact.put(i, count);
              }
  		}
  		if (N != 1) {
              primeFact.put((int)N, 1);
          }
  		return primeFact;
  	}
      */
  
      /* ------------------- Binary Search ------------------- */
      private static long factorial(int N) {
          long ans = 1L;
          for (int i = 2; i <= N; i++) {
              ans *= i;
          }
          return ans;
      }
  
      private static long[] factorialDP(int N) {
          long[] factDP = new long[N + 1];
          factDP[0] = factDP[1] = 1;
          for (int i = 2; i <= N; i++) {
              factDP[i] = factDP[i - 1] * i;
          }
          return factDP;
      }
  
      private static long factorialMod(int N, int mod) {
          long ans = 1L;
          for (int i = 2; i <= N; i++) {
              ans = ((ans % mod) * (i % mod)) % mod;
          }
          return ans;
      }
  
      /* ------------------- Binary Search ------------------- */
      private static int floorSearch(int[] arr, int st, int ed, int tar) {
          int ans = -1;
          while (st <= ed) {
              int mid = ((ed - st) >> 1) + st;
              if (arr[mid] <= tar) {
                  ans = mid;
                  st = mid + 1;
              } else {
                  ed = mid - 1;
              }
          }
          return ans;
      }
      
      private static int ceilingSearch(int[] arr, int st, int ed, int tar) {
          int ans = -1;
          while (st <= ed) {
              int mid = ((ed - st) >> 1) + st;
              if (arr[mid] < tar) {
                  st = mid + 1;
              } else {
                  ans = mid;
                  ed = mid - 1;
              }
          }
          return ans;
      }
      
      /* ------------------- Power Function ------------------- */
      public static long pow(long x, long y) {
          long res = 1;
  		while (y > 0) {
              if ((y & 1) != 0) {
                  res = (res * x);
  				y--;
  			}
  			x = (x * x);
  			y >>= 1;
  		}
  		return res;
  	}
      
  	public static long powMod(long x, long y, int mod) {
          long res = 1;
  		while (y > 0) {
              if ((y & 1) != 0) {
                  res = (res * x) % mod;
  				y--;
  			}
  			x = (x * x) % mod;
  			y >>= 1;
  		}
  		return res % mod;
  	}
  
      /* ------------------- Disjoint Set(Union and Find) ------------------- */
      private static class DSU {
  		public int[] parent, rank;
  		DSU(int N) {
  			parent = new int[N];
  			rank = new int[N];
  			for (int i = 0; i < N; i++) {
  				parent[i] = i;
                  rank[i] = 1;
              }
  		}
  		public int find(int a) {
  			if (parent[a] == a) {
  				return a;
              }
              return parent[a] = find(parent[a]);
  		}
  		public boolean union(int a, int b) {
  			int parA = find(a), parB = find(b);
  			if (parA == parB) return false;
  			if (rank[parA] > rank[parB]) {
                  parent[parB] = parA;
              } else if (rank[parA] < rank[parB]) {
                  parent[parA] = parB;
              } else {
                  parent[parA] = parB;
                  rank[parB]++;
              }
              return true;
  		}
  	}
      
      /* ------------------- Scanner class for input ------------------- */
      
      private static class FasterScanner {
  		private InputStream stream;
  		private byte[] buffer = new byte[1024];
  		private int curChar, numChars;
  		private SpaceCharFilter filter;
  
  		public FasterScanner() {
              // default
  			this.stream = System.in;
  		}
  
  		public FasterScanner(InputStream stream) {
  			this.stream = stream;
  		}
  
  		private int readChar() {
  			if (numChars == -1) {
  				throw new InputMismatchException();
              }
  			if (curChar >= numChars) {
  				curChar = 0;
  				try {
  					numChars = stream.read(buffer);
  				} catch (IOException e) {
  					throw new InputMismatchException(e.getMessage());
  				}
  				if (numChars <= 0) {
  					return -1;
                  }
  			}
  			return buffer[curChar++];
  		}
  
  		private boolean isWhiteSpace(int c) {
  			if (filter != null) {
  				return filter.isWhiteSpace(c);
              }
  			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
  		}
  
  		private boolean isNewLine(int ch) {
  			if (filter != null) {
  				return filter.isNewLine(ch);
              }
  			return ch == '\r' || ch == '\n' || ch == -1;
  		}
  
          public char nextChar() {
              int ch = readChar();
              char res = '\0';
              while (isWhiteSpace(ch)) {
                  ch = readChar();
              }
              do {
                  res = (char)ch;
                  ch = readChar();
              } while (!isWhiteSpace(ch));
              return res;
          }
  
  		public String next() {
  			int ch = readChar();
              StringBuilder res = new StringBuilder();
  			while (isWhiteSpace(ch)) {
  				ch = readChar();
              }
  			do {
  				res.appendCodePoint(ch);
  				ch = readChar();
  			} while (!isWhiteSpace(ch));
  			return res.toString();
  		}
  
  		public String nextLine() {
  			int ch = readChar();
              StringBuilder res = new StringBuilder();
  			do {
  				res.appendCodePoint(ch);
  				ch = readChar();
  			} while (!isNewLine(ch));
  			return res.toString();
  		}
  
  		public int nextInt() {
  			int ch = -1, sgn = 1, res = 0;
              do {
                  ch = readChar();
              } while (isWhiteSpace(ch));
  			if (ch == '-') {
  				sgn = -1;
  				ch = readChar();
  			}
  			do {
  				if (ch < '0' || ch > '9') {
  					throw new InputMismatchException("not a number");
                  }
  				res = (res * 10) + (ch - '0');
  				ch = readChar();
  			} while (!isWhiteSpace(ch));
              
  			return res * sgn;
  		}
  
  		public long nextLong() {
  			int ch = -1, sgn = 1;
              long res = 0L;
              do {
                  ch = readChar();
              } while (isWhiteSpace(ch));
  			if (ch == '-') {
  				sgn = -1;
  				ch = readChar();
  			}
  			do {
  				if (ch < '0' || ch > '9') {
  					throw new InputMismatchException("not a number");
                  }
  				res = (10L * res) + (ch - '0');
  				ch = readChar();
  			} while (!isWhiteSpace(ch));
  
  			return 1L * res * sgn;
  		}
  
          public double nextDouble() {
              return Double.parseDouble(next());
          }
  
          /* for custom delimiters */
  		public interface SpaceCharFilter {
  			public boolean isWhiteSpace(int ch);
  			public boolean isNewLine(int ch);
  		}
  	}
  }
  