#include <bits/stdc++.h>
using namespace std;
using namespace chrono;
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
void _print(unsigned long long t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
long long gcd(long long a, long long b) {
  if (b > a) {
    return gcd(b, a);
  }
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long expo(long long a, long long b, long long mod) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) res = (res * a) % mod;
    a = (a * a) % mod;
    b = b >> 1;
  }
  return res;
}
void extendgcd(long long a, long long b, long long *v) {
  if (b == 0) {
    v[0] = 1;
    v[1] = 0;
    v[2] = a;
    return;
  }
  extendgcd(b, a % b, v);
  long long x = v[1];
  v[1] = v[0] - v[1] * (a / b);
  v[0] = x;
  return;
}
long long mminv(long long a, long long b) {
  long long arr[3];
  extendgcd(a, b, arr);
  return arr[0];
}
long long mminvprime(long long a, long long b) { return expo(a, b - 2, b); }
bool revsort(long long a, long long b) { return a > b; }
void swap(int &x, int &y) {
  int temp = x;
  x = y;
  y = temp;
}
long long combination(long long n, long long r, long long m, long long *fact,
                      long long *ifact) {
  long long val1 = fact[n];
  long long val2 = ifact[n - r];
  long long val3 = ifact[r];
  return (((val1 * val2) % m) * val3) % m;
}
void google(int t) { cout << "Case #" << t << ": "; }
vector<long long> sieve(int n) {
  int *arr = new int[n + 1]();
  vector<long long> vect;
  for (int i = 2; i <= n; i++)
    if (arr[i] == 0) {
      vect.push_back(i);
      for (int j = 2 * i; j <= n; j += i) arr[j] = 1;
    }
  return vect;
}
long long mod_add(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a + b) % m) + m) % m;
}
long long mod_mul(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a * b) % m) + m) % m;
}
long long mod_sub(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a - b) % m) + m) % m;
}
long long mod_div(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (mod_mul(a, mminvprime(b, m), m) + m) % m;
}
long long phin(long long n) {
  long long number = n;
  if (n % 2 == 0) {
    number /= 2;
    while (n % 2 == 0) n /= 2;
  }
  for (long long i = 3; i <= sqrt(n); i += 2) {
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      number = (number / i * (i - 1));
    }
  }
  if (n > 1) number = (number / n * (n - 1));
  return number;
}
long long cmp(long long a, long long b) { return a > b; }
int isprime(int N) {
  if (N < 2 || (!(N & 1) && N != 2)) return 0;
  for (int i = 3; i * i <= N; i += 2) {
    if (!(N % i)) return 0;
  }
  return 1;
}
vector<long long> primeFactors(long long n) {
  vector<long long> factors;
  while (n % 2 == 0) {
    factors.push_back(2);
    n = n / 2;
  }
  for (int i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      factors.push_back(i);
      n = n / i;
    }
  }
  if (n > 2) factors.push_back(n);
  return factors;
}
long long power(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) {
      ans = (ans * a * 1LL);
    }
    a = (a * a * 1LL);
    b >>= 1;
  }
  return ans;
}
long long maxsubarraysum(long long *array, long long n) {
  long long best = 0, sum = 0;
  for (long long k = 0; k < n; k++) {
    sum = max(array[k], sum + array[k]);
    best = max(best, sum);
  }
  return best;
}
void printBinary(int num) {
  for (int i = 10; i >= 0; --i) {
    cout << ((num >> i) & 1);
  }
  cout << endl;
}
int computeXOR(int n) {
  if (n % 4 == 0) return n;
  if (n % 4 == 1) return 1;
  if (n % 4 == 2) return n + 1;
  return 0;
}
void solve() {
  long long n, h;
  cin >> n >> h;
  vector<long long> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  long long s = 1, l = 1e18;
  long long hc = h;
  while (s < l) {
    hc = h;
    long long m = (s + l) / 2;
    for (int i = 0; i < n - 1; i++) hc -= min(a[i + 1] - a[i], m);
    hc -= m;
    ;
    ;
    if (hc <= 0) {
      l = m;
    } else {
      s = m + 1;
    }
  }
  cout << s << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  auto start1 = high_resolution_clock::now();
  long long tc = 1;
  cin >> tc;
  for (int i = 1; i <= tc; i++) {
    solve();
  }
  auto stop1 = high_resolution_clock::now();
  auto duration = duration_cast<microseconds>(stop1 - start1);
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

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].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using namespace chrono;
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
void _print(unsigned long long t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
long long gcd(long long a, long long b) {
  if (b > a) {
    return gcd(b, a);
  }
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long expo(long long a, long long b, long long mod) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) res = (res * a) % mod;
    a = (a * a) % mod;
    b = b >> 1;
  }
  return res;
}
void extendgcd(long long a, long long b, long long *v) {
  if (b == 0) {
    v[0] = 1;
    v[1] = 0;
    v[2] = a;
    return;
  }
  extendgcd(b, a % b, v);
  long long x = v[1];
  v[1] = v[0] - v[1] * (a / b);
  v[0] = x;
  return;
}
long long mminv(long long a, long long b) {
  long long arr[3];
  extendgcd(a, b, arr);
  return arr[0];
}
long long mminvprime(long long a, long long b) { return expo(a, b - 2, b); }
bool revsort(long long a, long long b) { return a > b; }
void swap(int &x, int &y) {
  int temp = x;
  x = y;
  y = temp;
}
long long combination(long long n, long long r, long long m, long long *fact,
                      long long *ifact) {
  long long val1 = fact[n];
  long long val2 = ifact[n - r];
  long long val3 = ifact[r];
  return (((val1 * val2) % m) * val3) % m;
}
void google(int t) { cout << "Case #" << t << ": "; }
vector<long long> sieve(int n) {
  int *arr = new int[n + 1]();
  vector<long long> vect;
  for (int i = 2; i <= n; i++)
    if (arr[i] == 0) {
      vect.push_back(i);
      for (int j = 2 * i; j <= n; j += i) arr[j] = 1;
    }
  return vect;
}
long long mod_add(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a + b) % m) + m) % m;
}
long long mod_mul(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a * b) % m) + m) % m;
}
long long mod_sub(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (((a - b) % m) + m) % m;
}
long long mod_div(long long a, long long b, long long m) {
  a = a % m;
  b = b % m;
  return (mod_mul(a, mminvprime(b, m), m) + m) % m;
}
long long phin(long long n) {
  long long number = n;
  if (n % 2 == 0) {
    number /= 2;
    while (n % 2 == 0) n /= 2;
  }
  for (long long i = 3; i <= sqrt(n); i += 2) {
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      number = (number / i * (i - 1));
    }
  }
  if (n > 1) number = (number / n * (n - 1));
  return number;
}
long long cmp(long long a, long long b) { return a > b; }
int isprime(int N) {
  if (N < 2 || (!(N & 1) && N != 2)) return 0;
  for (int i = 3; i * i <= N; i += 2) {
    if (!(N % i)) return 0;
  }
  return 1;
}
vector<long long> primeFactors(long long n) {
  vector<long long> factors;
  while (n % 2 == 0) {
    factors.push_back(2);
    n = n / 2;
  }
  for (int i = 3; i <= sqrt(n); i = i + 2) {
    while (n % i == 0) {
      factors.push_back(i);
      n = n / i;
    }
  }
  if (n > 2) factors.push_back(n);
  return factors;
}
long long power(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) {
      ans = (ans * a * 1LL);
    }
    a = (a * a * 1LL);
    b >>= 1;
  }
  return ans;
}
long long maxsubarraysum(long long *array, long long n) {
  long long best = 0, sum = 0;
  for (long long k = 0; k < n; k++) {
    sum = max(array[k], sum + array[k]);
    best = max(best, sum);
  }
  return best;
}
void printBinary(int num) {
  for (int i = 10; i >= 0; --i) {
    cout << ((num >> i) & 1);
  }
  cout << endl;
}
int computeXOR(int n) {
  if (n % 4 == 0) return n;
  if (n % 4 == 1) return 1;
  if (n % 4 == 2) return n + 1;
  return 0;
}
void solve() {
  long long n, h;
  cin >> n >> h;
  vector<long long> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  long long s = 1, l = 1e18;
  long long hc = h;
  while (s < l) {
    hc = h;
    long long m = (s + l) / 2;
    for (int i = 0; i < n - 1; i++) hc -= min(a[i + 1] - a[i], m);
    hc -= m;
    ;
    ;
    if (hc <= 0) {
      l = m;
    } else {
      s = m + 1;
    }
  }
  cout << s << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  auto start1 = high_resolution_clock::now();
  long long tc = 1;
  cin >> tc;
  for (int i = 1; i <= tc; i++) {
    solve();
  }
  auto stop1 = high_resolution_clock::now();
  auto duration = duration_cast<microseconds>(stop1 - start1);
  return 0;
}

```