import sequtils,algorithm,math,tables import sets,intsets,queues,heapqueue,bitops,strutils template times*(n:int,body) = (for _ in 0.." .} proc scan(): int = while true: let k = getchar_unlocked() if k < '0': break result = 10 * result + k.ord - '0'.ord const INF = int.high div 4 proc powerWhenTooBig(x,n:int,modulo:int = 0): int = proc mul(x,n,modulo:int):int = if n == 0: return 0 if n == 1: return x result = mul(x,n div 2,modulo) mod modulo result = (result * 2) mod modulo result = (result + x * (n mod 2 == 1).int) mod modulo if n == 0: return 1 if n == 1: return x let pow_2 = powerWhenTooBig(x,n div 2,modulo) odd = if n mod 2 == 1: x else: 1 if modulo > 0: const maybig = int.high.float.sqrt.int div 2 if pow_2 > maybig or odd > maybig: result = mul(pow_2,pow_2,modulo) result = mul(result,odd,modulo) else: result = (pow_2 * pow_2) mod modulo result = (result * odd) mod modulo else: return pow_2 * pow_2 * odd proc millerRabinIsPrime(n:int):bool = # O(log n) proc ctz(n:int):int{.importC: "__builtin_ctzll", noDecl .} # 01<0000> -> 4 proc power(x,n:int,modulo:int = 0): int = if n == 0: return 1 if n == 1: return x let pow_2 = power(x,n div 2,modulo) result = pow_2 * pow_2 * (if n mod 2 == 1: x else: 1) if modulo > 0: result = result mod modulo if n <= 1 : return false if n div 2 == 0: return false if n == 2 or n == 3 or n == 5: return true let s = ctz(n - 1) d = (n - 1) div (1 shl s) var a_list = @[2, 7, 61] if n >= 4_759_123_141 and n < 341_550_071_728_321: a_list = @[2, 3, 5, 7, 11, 13, 17] if n in a_list : return true for a in a_list: if powerWhenTooBig(a,d,n) == 1 : continue let notPrime = toSeq(0..