Buggy python submission (verdict: Time Limit Exceeded):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce, lru_cache
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = 10**6#float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
#from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

N, A = MAP()
x = LIST()

dp = [[] for _ in range(sum(x)+1)]
dp[0].append(0)

for y in x:
	for i in range(sum(x)-y, -1, -1):
		if dp[i]:
			for z in dp[i]:
				dp[i+y].append(z+1)

ans = 0
for i in range(1, sum(x)//A + 1):
	ans += Counter(dp[i*A])[i]

print(ans)

Fixed submission:
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce, lru_cache
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = 10**6#float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
#from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

N, A = MAP()
x = LIST()

big = []
small = []
cnt = 0

for y in x:
	if y == A:
		cnt += 1
	elif y < A:
		small.append(A-y)
	else:
		big.append(y-A)

big_possible = [0]*2501
small_possible = [0]*2501
big_possible[0] = 1
small_possible[0] = 1

for a in big:
	for i in range(2500-a, -1, -1):
		if big_possible[i]:
			big_possible[i+a] += big_possible[i]

for b in small:
	for i in range(2500-b, -1, -1):
		if small_possible[i]:
			small_possible[i+b] += small_possible[i]

ans = 1
for i in range(1, 2501):
	ans += small_possible[i]*big_possible[i]


ans *= 2**cnt
print(ans-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

		
#階乗#
lim = 50  #必要そうな階乗の限界を入力
fact = [1] * (lim+1)
for n in range(1, lim+1):
	fact[n] = n * fact[n-1]

def C(n, r):
	return fact[n]//fact[r]//fact[n-r]

N, A = LIST()
x = LIST()

x_sum = sum(x)
x_cnt = Counter(x)
p = [[] for _ in range(x_sum+1)]  #p[i]はiを作ることが可能な数字の組み合わせ
p[0].append([])

for v in x:
	for i in range(x_sum, v-1, -1):
		if p[i-v]:
			for u in p[i-v]:
				y = u.copy()
				y.append(v)
				y.sort()
				if not y in p[i]:
					p[i].append(y)

ans = 0
for i in range(1, N+1):
	if x_sum < A*i:
		break
	for a in p[A*i]:
		if len(a) == i:
			cnt = 1
			for key, value in Counter(a).items():
				cnt *= C(x_cnt[key], value)
			ans += cnt


print(ans)

Fixed submission:
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce, lru_cache
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = 10**6#float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
#from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

N, A = MAP()
x = LIST()

big = []
small = []
cnt = 0

for y in x:
	if y == A:
		cnt += 1
	elif y < A:
		small.append(A-y)
	else:
		big.append(y-A)

big_possible = [0]*2501
small_possible = [0]*2501
big_possible[0] = 1
small_possible[0] = 1

for a in big:
	for i in range(2500-a, -1, -1):
		if big_possible[i]:
			big_possible[i+a] += big_possible[i]

for b in small:
	for i in range(2500-b, -1, -1):
		if small_possible[i]:
			small_possible[i+b] += small_possible[i]

ans = 1
for i in range(1, 2501):
	ans += small_possible[i]*big_possible[i]


ans *= 2**cnt
print(ans-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

		
#階乗#
lim = 50  #必要そうな階乗の限界を入力
fact = [1] * (lim+1)
for n in range(1, lim+1):
	fact[n] = n * fact[n-1]

def C(n, r):
	return fact[n]//fact[r]//fact[n-r]

N, A = LIST()
x = LIST()


x_cnt = Counter(x)
p = [[] for _ in range(sum(x)+1)]  #p[i]はiを作ることが可能な数字の組み合わせ
p[0].append([])

for v in x:
	for i in range(sum(x), v-1, -1):
		if p[i-v]:
			for u in p[i-v]:
				y = u.copy()
				y.append(v)
				y.sort()
				if not y in p[i]:
					p[i].append(y)

ans = 0
for i in range(1, N+1):
	if sum(x) < A*i:
		break
	for a in p[A*i]:
		if len(a) == i:
			cnt = 1
			for key, value in Counter(a).items():
				cnt *= C(x_cnt[key], value)
			ans += cnt


print(ans)

Fixed submission:
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce, lru_cache
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = 10**6#float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
#from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

N, A = MAP()
x = LIST()

big = []
small = []
cnt = 0

for y in x:
	if y == A:
		cnt += 1
	elif y < A:
		small.append(A-y)
	else:
		big.append(y-A)

big_possible = [0]*2501
small_possible = [0]*2501
big_possible[0] = 1
small_possible[0] = 1

for a in big:
	for i in range(2500-a, -1, -1):
		if big_possible[i]:
			big_possible[i+a] += big_possible[i]

for b in small:
	for i in range(2500-b, -1, -1):
		if small_possible[i]:
			small_possible[i+b] += small_possible[i]

ans = 1
for i in range(1, 2501):
	ans += small_possible[i]*big_possible[i]


ans *= 2**cnt
print(ans-1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

		
#階乗#
lim = 50  #必要そうな階乗の限界を入力
fact = [1] * (lim+1)
for n in range(1, lim+1):
	fact[n] = n * fact[n-1]

def C(n, r):
	return fact[n]//fact[r]//fact[n-r]

N, A = LIST()
x = LIST()


x_cnt = Counter(x)
p = [[] for _ in range(sum(x)+1)]  #p[i]はiを作ることが可能な数字の組み合わせ
p[0].append([])

for v in x:
	for i in range(sum(x), v-1, -1):
		if p[i-v]:
			for u in p[i-v]:
				y = u.copy()
				y.append(v)
				y.sort()
				if not y in p[i]:
					p[i].append(y)

ans = 0
for i in range(1, N+1):
	if sum(x) < A*i:
		break
	for a in p[A*i]:
		if len(a) == i:
			cnt = 1
			for key, value in Counter(a).items():
				cnt *= C(x_cnt[key], value)
			ans += cnt


print(ans)

Fixed submission:
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce, lru_cache
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = 10**6#float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
#from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10

N, A = MAP()
x = LIST()

big = []
small = []
cnt = 0

for y in x:
	if y == A:
		cnt += 1
	elif y < A:
		small.append(A-y)
	else:
		big.append(y-A)

big_possible = [0]*2501
small_possible = [0]*2501
big_possible[0] = 1
small_possible[0] = 1

for a in big:
	for i in range(2500-a, -1, -1):
		if big_possible[i]:
			big_possible[i+a] += big_possible[i]

for b in small:
	for i in range(2500-b, -1, -1):
		if small_possible[i]:
			small_possible[i+b] += small_possible[i]

ans = 1
for i in range(1, 2501):
	ans += small_possible[i]*big_possible[i]


ans *= 2**cnt
print(ans-1)