{
  "Greatest Common Divisor": {
    "prefix": "gcd",
    "body": [
      "int gcd(int a, int b)",
      "{",
      "    if (b == 0)",
      "        return a;",
      "    return gcd(b, a % b);",
      "     ",
      "}"
    ],
    "description": "GCD using Euclidean Algorithm"
  },
  "Maximum Function with long long int": {
    "prefix": "maxll",
    "body": [
      "long long int max(long long int a, long long int b)",
      "{",
      "    if (a >= b)",
      "    {",
      "        return a;",
      "    }",
      "    else",
      "    {",
      "        return b;",
      "    }",
      "}"
    ],
    "description": "Maximum Function with long long int"
  },
  "Minimum Function with long long int": {
    "prefix": "minll",
    "body": [
      "long long int min(long long int a, long long int b)",
      "{",
      "    if (a >= b)",
      "    {",
      "        return b;",
      "    }",
      "    else",
      "    {",
      "        return a;",
      "    }",
      "}"
    ],
    "description": "Minimum Function with long long int"
  },
  "Check number is power of two": {
    "prefix": "isPowerOfTwo",
    "body": [
      "bool isPowerOfTwo(int n) {",
      "  return n && (!(n & (n - 1)));",
      "}"
    ],
    "description": "Check number is power of two"
  },
  "Check number is prime": {
    "prefix": "isPrime",
    "body": [
      "bool isPrime(int n)",
      "{",
      "  for (int i = 2; i * i <= n; i++) {",
      "    if (n % i == 0)return false;",
      "  }",
      "  return true;",
      "}"
    ],
    "description": "Check number is prime"
  },
  "Return all prime factors": {
    "prefix": "primeFactors",
    "body": [
      "vector<int> primeFactors(int n)",
      "{",
      "  vector<int> v;",
      "  if (n % 2 == 0) {",
      "    v.push_back(2);",
      "    while (n % 2 == 0)n /= 2;",
      "  }",
      "  for (int i = 3; i * i <= n; i += 2) {",
      "    if (n % i == 0) {",
      "      v.push_back(i);",
      "      while (n % i == 0)n /= i;",
      "    }",
      "  }",
      "  if (n > 2)v.push_back(n);",
      "  return v;",
      "}"
    ],
    "description": "return all prime factors"
  },
  "Sum of all divisors": {
    "prefix": "divisorFunction",
    "body": [
      "//return sum all divisors",
      "int divisorFunction(int n)",
      "{",
      "  int ans = 1;",
      "  int power = 0;",
      "  while (n % 2 == 0)power++, n /= 2;",
      "  //sum of GP",
      "  ans *= (pow(2, power + 1) - 1);",
      "  for (int i = 3; i * i <= n; i += 2) {",
      "    power = 0;",
      "    while (n % i == 0) {",
      "      power++;",
      "      n /= i;",
      "    }",
      "    ans *= (pow(i, power + 1) - 1) / (i - 1);",
      "  }",
      "  return ans;",
      "}"
    ],
    "description": "sum of all divisors"
  },
  "Return n!": {
    "prefix": "nFactorial",
    "body": [
      "//when n! <1e18 and you need raw",
      "long long int nFactorial(int n)",
      "{",
      "  long long int ans = 1;",
      "  for (int i = 2; i <= n; i++)ans *= i;",
      "  return ans;",
      "}"
    ],
    "description": "return n!"
  },
  "Return n!%mod": {
    "prefix": "nFactorialMOD",
    "body": [
      "// n!%mod  ,for ex mod=1e9+7",
      "int nFactorialMOD(int n, int mod)",
      "{",
      "  int ans = 1;",
      "  for (int i = 2; i <= n; i++)(ans *= i) %= mod;",
      "  return ans;",
      "}"
    ],
    "description": "return n!%mod"
  },
  "Next power of two": {
    "prefix": "nextPowerOfTwo",
    "body": [
      "int nextPowerOfTwo(int n)",
      "{",
      "  //if n is power of two",
      "  if (n && (!n & (n - 1)))return n;",
      "  return 1 << ((int)ceil(log2(n)));",
      "}"
    ],
    "description": "next power of two"
  },
  "Prev power of two": {
    "prefix": "prevPowerOfTwo",
    "body": [
      "int prevPowerOfTwo(int n)",
      "{",
      "  //if n is power of two",
      "  if (n && (!n & (n - 1)))return n;",
      "  return 1 << ((int)ceil(log2(n) - 1));",
      "}"
    ],
    "description": "prev power of two"
  },
  "x^y": {
    "prefix": "xpowery",
    "body": [
      "long long int xpowery(long long int x,long long int y) {",
      "  long long int res = 1;",
      "  /*",
      "  it depends sometimes on questions too,",
      "  whether pow(0,0) is 1 or 0",
      "  So change accordingly",
      "  */",
      "  if (x == 0)return 0LL;",
      "  while (y)",
      "  {",
      "    if (y & 1)res *= x;",
      "    y >>= 1;",
      "    x *= x;",
      "  }",
      "  return res;",
      "}"
    ],
    "description": "x^y"
  },
  "(x^y)%mod": {
    "prefix": "xpoweryMOD",
    "body": [
      "long long int xpoweryMOD(long long int x,long long int y, int mod)",
      "{",
      "  long long int res = 1;",
      "  /*",
      "  it depends sometimes on questions too,",
      "  whether pow(0,0) is 1 or 0",
      "  So change accordingly",
      "  */",
      "  if (x == 0)return 0;",
      "  while (y)",
      "  {",
      "    if (y & 1)(res *= x) %= mod;",
      "    y >>= 1;",
      "    (x *= x) %= mod;",
      "  }",
      "  return res;",
      "}"
    ],
    "description": "(x^y)%mod"
  },
  "Sieve of eratosthenes": {
    "prefix": "sieve",
    "body": [
      "//return all primes b/w 1 to n",
      "vector<int> sieve(int n)",
      "{",
      "   vector<bool> is(n + 1, true);",
      "   vector<int> primes;",
      "   for (int i = 2; i * i <= n; i++) {",
      "      if (is[i]) {",
      "         for (int p = i * i; p <= n; p += i)is[p] = false;",
      "      }",
      "   }",
      "   for (int i = 2; i <= n; i++)",
      "      if (is[i])primes.push_back(i);",
      "   return primes;",
      "}"
    ],
    "description": "sieve of eratosthenes"
  },
  "LCM between two number": {
    "prefix": "lcm",
    "body": [
      "long long int gcd(long long int a, long long int b)",
      "{",
      "  if (b == 0)",
      "    return a;",
      "  return gcd(b, a % b);",
      "}",
      "long long int lcm(int a, int b)",
      "{",
      "    return (a / gcd(a, b)) * b;",
      "}"
    ],
    "description": "Least Common Multiple"
  },
  "Combinatorics": {
    "prefix": "combinatorics",
    "body": [
      "int SIZE = 2000005;",
      "vector<int> fact(SIZE, 1);",
      "vector<int> inv(SIZE, 1);",
      "int inverse(int x, int y)",
      "{",
      "   int res = 1;",
      "   while (y) {",
      "      if (y & 1)res = (1LL * res * x) % MOD;",
      "      y >>= 1;",
      "      x = (1LL * x * x) % MOD;",
      "   }",
      "   return res;",
      "}",
      "void initCombinatorics()",
      "{",
      "   for (int i = 2; i < SIZE; i++) {",
      "      fact[i] = (1LL * fact[i - 1] * i) % MOD;",
      "      inv[i] = inverse(fact[i], MOD - 2);",
      "   }",
      "}",
      "int nCr(int n, int r)",
      "{",
      "   int res = 1;",
      "   if (r > n)return 0;",
      "   res = (1LL * fact[n] * inv[r]) % MOD;",
      "   res = (1LL * res * inv[n - r]) % MOD;",
      "   return res;",
      "}"
    ],
    "description": "Combinatorics"
  }
}