Problem:


Score : 300 points

Problem Statement

There is a box containing N balls. The i-th ball has the integer A_i written on it.
Snuke can perform the following operation any number of times:

Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.

Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \leq K \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print POSSIBLE; if it is not possible, print IMPOSSIBLE.

Sample Input 1

3 7
9 3 4

Sample Output 1

POSSIBLE

First, take out the two balls 9 and 4, and return them back along with a new ball, abs(9-4)=5.
Next, take out 3 and 5, and return them back along with abs(3-5)=2.
Finally, take out 9 and 2, and return them back along with abs(9-2)=7.
Now we have 7 in the box, and the answer is therefore POSSIBLE.

Sample Input 2

3 5
6 9 3

Sample Output 2

IMPOSSIBLE

No matter what we do, it is not possible to have 5 in the box. The answer is therefore IMPOSSIBLE.

Sample Input 3

4 11
11 3 7 15

Sample Output 3

POSSIBLE

The box already contains 11 before we do anything. The answer is therefore POSSIBLE.

Sample Input 4

5 12
10 2 8 6 4

Sample Output 4

IMPOSSIBLE



Sample input:
3 7
9 3 4


Sample output:
POSSIBLE

Submission status: Accepted

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz')
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main
    #%%
    N, K = R()
    A = R()
    if K > max(A):
        print('IMPOSSIBLE')
        return
    a = gcds(A)
    ak = gcds(A+[K])
    if a == 1:
        print('POSSIBLE')
    else:
        if a == ak:
            print('POSSIBLE')
        else:
            print('IMPOSSIBLE')

    #%%
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
#!/usr/bin/python3
# -*- coding:utf-8 -*-

from functools import reduce

def calc_gcd(a, b):
  if a > b:
    a, b = b, a
  while b % a:
    a, b = b % a, a
  return a

def main():
  n, k = map(int, input().split())
  la = list(map(int, input().split()))
  if max(la) >= k and k % (reduce(calc_gcd, la)) == 0:
    print('POSSIBLE')
  else:
    print('IMPOSSIBLE')
  
if __name__=='__main__':
  main()

Submission status: Accepted

Solution code:
import math

N, K = map(int,input().split(' '))
A = list(map(int,input().split(' ')))

A.sort()
A.reverse()

t=A[0]

def myGCD(a,b):
    while b!=0:
        a,b=b,a%b 
    return(a)   

for i in range(1,N):
    t=myGCD(t,A[i])

if K > A[0]:
    print("IMPOSSIBLE")
else:
    if K%t==0:
        print("POSSIBLE")
    else:
        print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
from fractions import gcd
n,k = map(int,input().split())
a = list(map(int,input().split()))
g = a[0]
for i in range(n):
  g = gcd(g,a[i])
if k%g == 0 and k <= max(a):
  print("POSSIBLE")
else:
  print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
import fractions
N,K=map(int,input().split())
L=list(map(int,input().split()))
tmp=0
if N==1:
	if L[0]==K:
		print("POSSIBLE")
		exit()
	else:
		print("IMPOSSIBLE")
		exit()
for i in range(1,N):
	if i==1:
		tmp=fractions.gcd(L[0],L[1])
	else:
		tmp=fractions.gcd(tmp,L[i])
if max(L)>=K and K%tmp==0:
	print("POSSIBLE")
else:
	print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
from collections import Counter,defaultdict,deque
from heapq import heappop,heappush,heapify
import sys,bisect,math,itertools,fractions
sys.setrecursionlimit(10**8)
mod = 10**9+7
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))

n,m = inpl()
a = inpl()
g = a[0]
for i in range(1,n):
    g = fractions.gcd(g,a[i])
if max(a) >= m and m % g == 0:
    print('POSSIBLE')
else:
    print('IMPOSSIBLE')

Submission status: Accepted

Solution code:
n, k = map(int, input().split())
A = list(map(int, input().split()))

# 最大公約数
def gcd(a, b):
	while b:
		a, b = b, a % b
	return a

MAX = max(A)
GCD = 0
for i in range(n):
	GCD = gcd(GCD, A[i])

if k % GCD == 0 and k <= MAX:
	print('POSSIBLE')
else:
	print('IMPOSSIBLE')

Submission status: Accepted

Solution code:
n, k = map(int, input().split())
A = list(map(int, input().split()))

import fractions
#import math
from functools import reduce

def gcd(*numbers):
    return reduce(fractions.gcd, numbers)
    #return reduce(math.gcd, numbers)

def gcd_list(numbers):
    return reduce(fractions.gcd, numbers)
    #return reduce(math.gcd, numbers)

g = gcd_list(A)
if k%g == 0 and max(A) >= k:
    print('POSSIBLE')
else:
    print('IMPOSSIBLE')

Submission status: Accepted

Solution code:
n, k = list(map(int, input().split()))
al = list(map(int, input().split()))
flag = True
for a in al:
    if a >= k:
        flag = False
if flag:
    print('IMPOSSIBLE')
    exit()
# a,bの最大公約数


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


t = al[0]
for i in range(1, n):
    t = gcd(t, al[i])


for a in al:
    if abs(k-a) % t == 0:
        print('POSSIBLE')
        exit()
print('IMPOSSIBLE')

Submission status: Accepted

Solution code:
n,k=map(int,input().split())
a=list(map(int,input().split()))
if k>max(a):
  print("IMPOSSIBLE")
  exit(0)

from fractions import gcd
gcd_v=a[0]
for i in range(1,n):
  gcd_v=gcd(a[i],gcd_v)
for aa in a:
  if (aa-k)%gcd_v==0:
    print("POSSIBLE")
    exit(0)
print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
n,k = map(int,input().split())

al = list(map(int,input().split()))


# a,bの最大公約数
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


# a,bの最小公倍数
def lcm(a, b):
    return a * b // gcd(a, b)


ans = al[0]

for a in al:
    ans = gcd(a, ans)

if k % ans == 0 and k <= max(al):
    print("POSSIBLE")
else:
    print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
N,K = map(int, input().split())
A = list(map(int, input().split()))


#２整数の最大公約数を求める

def gcd2(x,y): 
	while y != 0:
		x , y = y , x % y 
	return x



#N 整数の最大公約数を求める
#A = [A[0],...,A[N]] とする

def gcd(A):
    ans = A[0]
    for i in range(1,N): #range(1,N)= 1,2,...,N-1
        ans = gcd2(ans, A[i])
    return ans



g = gcd(A)
M = max(A)

if (K<= M) and (K%g == 0):
    print("POSSIBLE")
else: print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
from fractions import gcd
# from math import gcd

N, K = map(int, input().split())
A = list(map(int, input().split()))

M = max(A)

g = A[0]
for a in A:
    g = gcd(g, a)

if K <= M and K % g == 0:
    print ('POSSIBLE')
else:
    print ('IMPOSSIBLE')

Submission status: Accepted

Solution code:
N, K = map(int, input().split())
A = list(map(int, input().split()))
if K in A:
    print("POSSIBLE")
    exit()
if max(A) < K or N == 1:
    print("IMPOSSIBLE")
    exit()

A.sort()
for i in range(1, N):
    tmp = abs(A[i - 1] - A[i])
    if not tmp == 0 and K % tmp == 0:
        print("POSSIBLE")
        exit()
print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
import functools
from fractions import gcd
n,k = map(int,input().split())
li = list(map(int,input().split()))
g = functools.reduce(gcd,li)
if k > max(li):
    print("IMPOSSIBLE")
elif g == 1:
    print("POSSIBLE")
else:
    if k % g == 0:
        print("POSSIBLE")
    else:
        print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10 ** 5 + 10)
def input(): return sys.stdin.readline().strip()

def resolve():

    n,k=map(int,input().split())
    A=list(map(int,input().split()))

    from functools import reduce
    from fractions import gcd
    G=reduce(gcd,A)

    if k%G==0 and k<=max(A):
        print('POSSIBLE')
    else:
        print('IMPOSSIBLE')

resolve()

Submission status: Accepted

Solution code:
from fractions import gcd
N,K=map(int, input().split())
A=list(map(int, input().split()))
if K in A:
    print("POSSIBLE")
    exit()
if K>max(A):
    print("IMPOSSIBLE")
    exit()

for i in range(N-1):
    if i==0:
        G=gcd(A[0],A[1])
    else:
        G=gcd(G, A[i+1])
#print(G)
if K%G==0:
    print("POSSIBLE")
else:
    print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
N, K = map(int, input().split())
A = list(map(int, input().split()))

def gcd(n, m):
    if m == 0:
        return n
    return gcd(m, n % m)

G = A[0]
for a in A:
    G = gcd(G, a)

for a in A:
    if K <= a and (a - K) % G == 0:
        print('POSSIBLE')
        exit()

print('IMPOSSIBLE')

Submission status: Accepted

Solution code:
def gcd(x,y):
    while y>0:
        x,y = y,x%y
    return x
N,K = map(int,input().split())
A = sorted(list(map(int,input().split())))
a = A[0]
for i in range(1,N):
    a = gcd(a,A[i])
if K<=A[-1] and K%a==0:
    print("POSSIBLE")
else:
    print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
#%% for atcoder uniittest use
import sys
input= lambda: sys.stdin.readline().rstrip()
def pin(type=int):return map(type,input().split())
def tupin(t=int):return tuple(pin(t))
#%%code
from fractions import gcd
from functools import reduce
def resolve():
    N,K=pin()
    A=list(pin())
    A.sort()
    maxK=A[-1]
    step=reduce(gcd,A)
    cond=1
    if K>maxK or (maxK-K)%step!=0:cond=0
    print(["IMPOSSIBLE","POSSIBLE"][cond])

#%%submit!
resolve()

Submission status: Accepted

Solution code:
def main():
    N, K = (int(i) for i in input().split())
    A = [int(i) for i in input().split()]
    A.sort()
    maxA = A.pop()
    if maxA < K:
        return print("IMPOSSIBLE")
    if N == 1:
        if maxA == K:
            return print("POSSIBLE")
        else:
            return print("IMPOSSIBLE")
    g = A[0]

    def gcd(x, y):
        if y == 0:
            return x
        while y != 0:
            x, y = y, x % y
        return x

    for a in A[1:]:
        g = gcd(g, a)

    if (maxA - K) % g == 0:
        print("POSSIBLE")
    else:
        print("IMPOSSIBLE")


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N,K=map(int, input().split())
*A,=map(int, input().split())
def gcd(a,b):
    while b: a,b=b,a%b
    return a
g=0
for a in A: g=gcd(g,a)
print('POSSIBLE' if K%g==0 and K<=max(A) else 'IMPOSSIBLE')

Submission status: Accepted

Solution code:
def gcd(a: int, b: int) -> int:
    """a, bの最大公約数(greatest common divisor: GCD)を求める
    計算量: O(log(min(a, b)))
    """
    while b:
        a, b = b, a % b
    return a


def lcm(a: int, b: int) -> int:
    """a, bの最小公倍数(least common multiple: LCM)を求める
    計算量: O(log(min(a, b)))
    """
    return (a * b) // gcd(a, b)


def multi_gcd(array: list) -> int:
    """arrayのGCDを求める"""
    n = len(array)
    ans = array[0]
    for i in range(1, n):
        ans = gcd(ans, array[i])
    return ans


n, k = map(int, input().split())
a = list(map(int, input().split()))

gcd_ = multi_gcd(a)
if k % gcd_ == 0 and k <= max(a):
    print("POSSIBLE")
else:
    print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
def gcd(a,b):
  while b:a,b=b,a%b
  return a
n,k=map(int,input().split())
a=list(map(int,input().split()))
g=a[0]
for i in a[1:]:g=gcd(g,i)
ans="IMPOSSIBLE"
for i in a:
  if k>i:continue
  if abs(k-i)%g==0:ans="POSSIBLE"
print(ans)

Submission status: Accepted

Solution code:
from statistics import median
#import collections
#aa = collections.Counter(a) # list to list || .most_common(2)で最大の2個とりだせるお a[0][0]
from fractions import gcd
from itertools import combinations # (string,3) 3回
from collections import deque
from collections import defaultdict
import bisect
#
#    d = m - k[i] - k[j]
#    if kk[bisect.bisect_right(kk,d) - 1] == d:
#
#
#
# pythonで無理なときは、pypyでやると正解するかも！！
#
#

import sys
sys.setrecursionlimit(10000000)
mod = 10**9 + 7

def readInts():
  return list(map(int,input().split()))
def main():
    n,k = readInts()
    A = readInts()
    g = 0
    for i in range(n):
        g = gcd(g,A[i])

    if k <= max(A) and k % g == 0:
        print("POSSIBLE")
    else:
        print('IMPOSSIBLE')
if __name__ == '__main__':
  main()

Submission status: Accepted

Solution code:
n,k=map(int,input().split())
a=list(map(int,input().split()))
if k> max(a):
    print('IMPOSSIBLE')
    exit()
import fractions
b=a[0]
for i in range(1,n):
    b=fractions.gcd(b,a[i])
print('POSSIBLE' if k%b==0 else 'IMPOSSIBLE')

Submission status: Accepted

Solution code:
N, K = map(int, input().split())
A = list(map(int, input().split()))

A = list(set(A))
N = len(A)
A.sort()

if K > max(A):
    print("IMPOSSIBLE")
    exit()

if N == 1:
    if A[0] == K:
        print("POSSIBLE")
    else:
        print("IMPOSSIBLE")
    exit()

min_diff = min([A[i] - A[i-1] for i in range(1,N)])

for i in range(N):
    if abs(A[i]-K) % min_diff == 0:
        print("POSSIBLE")
        break
else:
    print("IMPOSSIBLE")

Submission status: Accepted

Solution code:
import fractions
n,k = map(int,input().split())
ai = [int(i) for i in input().split()]

if n == 1:
    if k == ai[0]:
        print('POSSIBLE')
        exit()
    else:
        print('IMPOSSIBLE')
        exit()

g = fractions.gcd(ai[0],ai[1])

for i in range(1,n-1):
    #print(i)
    g = fractions.gcd(g,ai[i+1])

if k % g == 0 and max(ai) >= k:
    print('POSSIBLE')
else:
    print('IMPOSSIBLE')

Submission status: Accepted

Solution code:
from fractions import gcd
from functools import reduce

N, K = map(int, input().split())
A = list(map(int, input().split()))
G = reduce(gcd, A)
print("POSSIBLE" if K%G == 0 and K <= max(A) else "IMPOSSIBLE")

Submission status: Accepted

Solution code:
printn = lambda x: print(x,end='')
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
ins = lambda : input().strip()
DBG = True # and False
BIG = 10**18
R = 10**9 + 7

def ddprint(x):
  if DBG:
    print(x)

import fractions
n,k = inm()
a = inl()
#g = reduce(fractions.gcd,a)
g = a[0]
for i in range(1,n):
    g = fractions.gcd(g,a[i])
print('POSSIBLE' if k%g==0 and k<=max(a) else 'IMPOSSIBLE')

Submission status: Accepted

Solution code:
from fractions import gcd

N,K = map(int,input().split())
A = [int(i) for i in input().split()]

if K > max(A):
    print('IMPOSSIBLE')
    exit()


a = 0
for i in range(N):
    a = gcd(a,A[i])

if K % a == 0:
    print('POSSIBLE')
else:
    print('IMPOSSIBLE')

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10 ** 5 + 10)
def input(): return sys.stdin.readline().strip()

def resolve():

    N,K=map(int,input().split())
    A=list(map(int,input().split()))

    ma=max(A)

    from functools import reduce
    from fractions import gcd

    g=reduce(gcd,A)
    if K%g==0 and K<=ma:
        print('POSSIBLE')
    else: print('IMPOSSIBLE')

resolve()

Submission status: Accepted

Solution code:
from fractions import gcd
from functools import reduce
N,K,*A = map(int, open(0).read().split())
g = reduce(gcd,A)
a = max(A)
if a>=K and K%g==0:
  print('POSSIBLE')
else:
  print('IMPOSSIBLE')

Submission status: Accepted

Solution code:
from fractions import gcd
def agc018_a():
  n, k = map(int, input().split())
  A = list(map(int, input().split()))
  A = sorted(A)
  # 元の数列の最大を超える数は作れない
  if A[-1] < k:
    print('IMPOSSIBLE')
    return
  # 数列要素のgcdを求める
  g = A[0]
  for a in A:
    g = gcd(g, a)
    # 元の数列内に存在していれば即OK
    if a == k:
      print('POSSIBLE')
      return
  # gcdで割れる値なら作り出せる？？
  if k % g == 0:
    print('POSSIBLE')
  else:
    print('IMPOSSIBLE')

agc018_a()

Submission status: Accepted

Solution code:
import sys

sys.setrecursionlimit(10 ** 7)
f_inf = float('inf')
mod = 10 ** 9 + 7


def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a


def resolve():
    n, k = map(int, input().split())
    A = sorted(list(map(int, input().split())))

    if k in set(A):
        print("POSSIBLE")
        exit()

    if k > A[-1]:
        print("IMPOSSIBLE")
        exit()

    if n == 1:
        print("IMPOSSIBLE")
        exit()

    g = A[0]
    for i in range(1, n):
        g = gcd(g, A[i])

    if k % g == 0:
        print("POSSIBLE")
    else:
        print("IMPOSSIBLE")


if __name__ == '__main__':
    resolve()