Problem:


Score : 600 points

Problem Statement

Given are a sequence of N positive integers A_1, A_2, \ldots, A_N and another positive integer S.

For a non-empty subset T of the set \{1, 2, \ldots , N \}, let us define f(T) as follows:

f(T) is the number of different non-empty subsets \{x_1, x_2, \ldots , x_k \} of T such that A_{x_1}+A_{x_2}+\cdots +A_{x_k} = S.

Find the sum of f(T) over all 2^N-1 subsets T of \{1, 2, \ldots , N \}. Since the sum can be enormous, print it modulo 998244353.

Constraints

All values in input are integers.

1 \leq N \leq 3000

1 \leq S \leq 3000

1 \leq A_i \leq 3000

Input

Input is given from Standard Input in the following format:

N S
A_1 A_2 ... A_N

Output

Print the sum of f(T) modulo 998244353.

Sample Input 1

3 4
2 2 4

Sample Output 1

6

For each T, the value of f(T) is shown below. The sum of these values is 6.

f(\{1\}) = 0

f(\{2\}) = 0

f(\{3\}) = 1 (One subset \{3\} satisfies the condition.)

f(\{1, 2\}) = 1 (\{1, 2\})

f(\{2, 3\}) = 1 (\{3\})

f(\{1, 3\}) = 1 (\{3\})

f(\{1, 2, 3\}) = 2 (\{1, 2\}, \{3\})

Sample Input 2

5 8
9 9 9 9 9

Sample Output 2

0

Sample Input 3

10 10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

3296



Sample input:
3 4
2 2 4


Sample output:
6

Submission status: Runtime Error

Solution code:
def main():
	import sys
	sys.setrecursionlimit=10**7
	mod=998244353
	n,s=map(int,input().split())
	a=list(map(int,input().split()))
	from functools import lru_cache
	@lru_cache(maxsize=None)
	def dfs(x,y):
		if x==0:
			if y==0:
				return 1
			else:
				return 0
		r=dfs(x-1,y)*2%mod
		if y>0:
			if y-a[x-1]>=0:
				r+=dfs(x-1,y-a[x-1])
		r%=mod
		return r
	print(dfs(n,s))
main()

Submission status: Runtime Error

Solution code:
def main():
	import sys
	sys.setrecursionlimit=10**6
	mod=998244353
	n,s=map(int,input().split())
	a=list(map(int,input().split()))
	from functools import lru_cache
	@lru_cache(maxsize=None)
	def dfs(x,y):
		if x==0:
			if y==0:
				return 1
			else:
				return 0
		r=dfs(x-1,y)*2%mod
		if y>0:
			if y-a[x-1]>=0:
				r+=dfs(x-1,y-a[x-1])
		r%=mod
		return r
	print(dfs(n,s))
main()

Submission status: Runtime Error

Solution code:
mod = 998244353
n, s = map(int, input().split())
dp = np.zeros((n+1, s+1), dtype=int)
dp[0, 0] = 1
for i, a in enumerate(map(int, input().split())):
  dp[i+1] = dp[i] * 2 % mod
  dp[i+1][a:] = (dp[i+1][a:] + dp[i][:-a]) % mod
print(dp[-1, -1])

Submission status: Runtime Error

Solution code:
def main():
    n, s = map(int, input().split())
    mod = 998244353
    a = list(map(int, input().split()))
    dp = [[0]*(s+1) for _ in range(n+1)]
    dp[0][0] = 1
    dio = dp[0]
    for i in range(1, n+1):
        ai = a[i-1]
        di = dp[i]
        for j in range(max(s+1, ai)):
            di[j] += 2*dio[j]
            di[j] %= mod
        for j in range(ai, s+1):
            di[j] += dio[j-ai]
            di[j] %= mod
        dp[i] = di
        dio = di
    print(dp[n][s])
    

if __name__ == "__main__":
    main()

Submission status: Runtime Error

Solution code:
mod = 998244353

N, S, *A = map(int, open(0).read().split())

dp = [[0] * (S + 1) for _ in range(N + 1)]
dp[0][0] = 1

for i, a in enumerate(A, 1):
    for j in range(S + 1):
        dp[i][j] = 2 * dp[i - 1][j] + dp[i - 1][j - a] * (j >= a)

print(dp[N][S])

Submission status: Runtime Error

Solution code:
mod = 998244353

N, S, *A = map(int, open(0).read().split())

dp = [1] + [0] * S
for i, a in enumerate(A):
    for j in reversed(range(S + 1)):
        dp[j] = (2 * dp[j] + dp[j - a] * (j >= a)) % mod

print(dp[S])

Submission status: Runtime Error

Solution code:
mod = 998244353

N, S, *A = map(int, open(0).read().split())

dp = [1] + [0] * S
for i, a in enumerate(A):
    for j in reversed(range(S + 1)):
        dp[j] = 2 * dp[j] + dp[j - a] * (j >= a)

print(dp[S])

Submission status: Runtime Error

Solution code:
N, S = map(int, input().split())
A = list(int(x) for x in input().split())
MOD = 998244353

dp = [[0] * (S+1) for _ in range(N+1)]
dp[0][0] = 1

for i in range(N):
    for j in range(S+1):
        print(i, j)
        # 1,2のケース。jが変わらない遷移が2通りある。
        dp[i+1][j] += dp[i][j] * 2
        # 3のケース。j+A[i] <= Sならば、j+A[i]に遷移する。
        if j + A[i] <= S:
            dp[i+1][j+A[i]] += dp[i][j]
        print(dp)
print(dp[N][S])

Submission status: Runtime Error

Solution code:
import numpy as np

N,S,*A = map(int, open(0).read().split())
b = [x for x in A if x <= S]
coe = np.zeros(S+1,dtype='int64')
coe[0] = 2
coe[b[0]] = 1
for x in b[1:]:
    t1 = np.zeros(S+1,dtype='int64')
    t2 = np.zeros(S+1,dtype='int64')
    for i in range(S+1):
        if i + x <= S:
            t1[i] = (coe[i]*2) % 998244353
            t2[i+x] = coe[i]
        else:
            t1[i] = (coe[i]*2) % 998244353
    coe = t1 + t2
print(coe[S])

Submission status: Runtime Error

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

def solve(length, target, nums):
  
  dp = [[0]*(target+1)]*(length+1)
  
  for i, n in enumerate(nums):
    for j, comb_num in enumerate(dp[i]):
      sub = j - n
      dp[i + 1][j] += comb_num
      if sub >= 0::
        dp[i + 1][j] += dp[i][sub]
        
  print(dp[length][target])
  
solve(N, S, A)

Submission status: Runtime Error

Solution code:
import sys
sys.setrecursionlimit(10000000)
MOD = 998244353
INF = 10 ** 15

def main():
    N,S = map(int,input().split())
    A = list(map(int,input().split()))

    dp = [[0]*(1 + S) for _ in range(N + 1)]
    dp[0][0] = pow(2,N,MOD)
    inv2 = pow(2,MOD - 2,MOD)
    for i,a in enumerate(A):
        for j in range(a):
            dp[i + 1][j] = dp[i][j]
        for j in range(a,S + 1):
            dp[i + 1][j] = (dp[i][j] + dp[i][j - a] * inv2)%MOD
    print(dp[N][S])
if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
# coding: utf-8
#import numpy as np
import re
import math
from collections import defaultdict
from collections import deque
import collections
from fractions import Fraction
import bisect
from queue import PriorityQueue
import itertools
from copy import deepcopy
import random
import time
import os
import sys
import datetime
from functools import lru_cache
from functools import reduce
readline=sys.stdin.readline
sys.setrecursionlimit(2000000)
alphabet="abcdefghijklmnopqrstuvwxyz"
numbers="0123456789"
mod=int(10**9+7)
inf=int(10**19)
class Edge():
    def __init__(self,x,y,val=1):
        self.x=x
        self.y=y
        self.val=val
class unionfind():
    def __init__(self,n):
        self.n=n
        self.P=[a for a in range(n)]
        self.rank=[0]*n
 
    def find(self,x):
        if(x!=self.P[x]):
            self.P[x]=self.find(self.P[x])
        return self.P[x]
 
    def same(self,x,y):
        return self.find(x)==self.find(y)
 
    def link(self,x,y):
        if self.rank[x]<self.rank[y]:
            self.P[x]=y
        elif self.rank[y]<self.rank[x]:
            self.P[y]=x
        else:
            self.P[x]=y
            self.rank[y]+=1
 
    def unite(self,x,y):
        self.link(self.find(x),self.find(y))
 
    def size(self):
        S=set()
        for a in range(self.n):
            S.add(self.find(a))
        return len(S)
def yn(b):
    if b:print("yes")
    else:print("no")
def Yn(b):
    if b:print("Yes")
    else:print("No")
def YN(b):
    if b:print("YES")
    else:print("NO")
def ispow(a,b):
    now=b
    while now<a:
        now*=b
    return now==a
def getbin(num,size):
    A=[0]*size
    for a in range(size):
        if (num>>(size-a-1))&1==1:
            A[a]=1
        else:
            A[a]=0
    return A
def getfacs(n,mod_=0):
    A=[1]*(n+1)
    for a in range(2,len(A)):
        A[a]=A[a-1]*a
        if(mod_>0):A[a]%=mod_
    return A
def comb(n,r,mod,fac):
    if(n-r<0):return 0
    return (fac[n]*pow(fac[n-r],mod-2,mod)*pow(fac[r],mod-2,mod))%mod
def nextcomb(num,size):
    x=num&(-num)
    y=num+x
    z=num&(~y)
    z//=x
    z=z>>1
    num=(y|z)
    if(num>=(1<<size)):return False
    else:return num
def getprimes(n):
    if n==0:return []
    A=[True]*(n+1)
    A[0]=False
    A[1]=False
    for a in range(2,n+1):
        if A[a]:
            for b in range(a*2,n+1,a):
                A[b]=False
    ret=[]
    for a in range(n+1):
        if(A[a]):ret.append(a)
    return ret
def isprime(num):
    if(num<=1):return False
    i=2
    while i*i<=num:
       if(num%i==0):return False
       i+=1
    return True
def ifelse(bbool,ret1,ret2):
    if bbool:return ret1
    else:return  ret2
def join(A,c=" "):
    n=len(A)
    A=list(map(str,A))
    s=""
    for a in range(n):
        s+=A[a]
        if(a<n-1):s+=c
    return s
def factorize(n):
    b = 2
    ret=defaultdict(int)
    while b * b <= n:
        while n % b == 0:
            n //= b
            ret[b]+=1
        b+=1
    if n > 1:ret[n]+=1
    return ret
def pm(x):
    return x//abs(x)
def inputintlist(): 
    return list(map(int,input().split()))
def inputfloatlist(): 
    return list(map(float,input().split()))
def tozero(A):
    ret=[None]*len(A)
    for a in range(len(A)):
        ret[a]=A[a]-1
    return ret
def istanchouzouka(A):
    f=True
    prev=min(A)-1
    for a in A:
        if prev>=a:
            f=False
        prev=a
    return f
def istanchouhigensyou(A):
    f=True
    prev=min(A)-1
    for a in A:
        if prev>a:
            f=False
        prev=a
    return f
def getallsum(A):
    s=sum(A)
    dp=defaultdict(int)
    dp[0]=1
    for a in range(0,len(A)):
        for b in range(s,-1,-1):
            if b-A[a]>=0:
                dp[b]+=dp[b-A[a]]
    return dp
def yuukoutomukou(edges):
    ret=deepcopy(edges)
    for edge in edges:
        if not edge.x==edge.y:
            ret.append(Edge(edge.y,edge.x,edge.val))
    return ret
def dijkstra(edges,V,start):
    mincost=[inf]*V
    G=[[] for a in range(V)]
    for edge in edges:
        G[edge.x].append([edge.val,edge.y])
    Q=PriorityQueue()
    Q.put([0,start])#[cost,x]
    while not Q.empty():
        nowcost,nowx=Q.get()
        if mincost[nowx]==inf:
            mincost[nowx]=nowcost
            for cost,y in G[nowx]:
                newcost=nowcost+cost
                Q.put([newcost,y])
    return mincost
def warshallfloyd(edges,V):
    mincost=[[inf for b in range(V)] for a in range(V)]
    for a in range(V):mincost[a][a]=0
    for edge in edges:
        mincost[edge.x][edge.y]=min(mincost[edge.x][edge.y],edge.val)#x→yが複数ある場合のためにmin()する
    for k in range(V):
        for s in range(V):
            for t in range(V):
                if mincost[s][k]==inf or mincost[k][t]==inf:continue
                mincost[s][t]=min(mincost[s][t],mincost[s][k]+mincost[k][t])
    return mincost
def bellemanford(edges,V,start):
    mincost=[inf]*V
    mincost[start]=0
    for _ in range(V):
        for edge in edges:
            if mincost[edge.x]==inf:continue
            mincost[edge.y]=min(mincost[edge.y],mincost[edge.x]+edge.val)
    return mincost
def ruisekiwa(A):
    ret=[0]*(len(A)+1)
    for a in range(len(A)):
        ret[a+1]=ret[a]+A[a]
    return ret
def getmd(x1,y1,x2,y2):
    return abs(x1-x2)+abs(y1-y2)
def geted(x1,y1,x2,y2):
    return math.sqrt((x1-x2)**2+(y1-y2)**2)
class fordfulkerson():
    def __init__(self,edges,V,s,t):
        self.V=V
        self.used=[False]*V
        self.G=[[] for a in range(V)]
        self.s=s
        self.t=t
        for edge in edges:
            self.G[edge.x].append({"x":edge.x,"y":edge.y,"cap":edge.val,"rev":len(self.G[edge.y])})
            self.G[edge.y].append({"x":edge.y,"y":edge.x,"cap":0,"rev":len(self.G[edge.x])-1})
    def dfs(self,v,t,f=inf):
        if v==t:return f
        self.used[v]=True
        for a in range(len(self.G[v])):
            x=self.G[v][a]["x"]
            y=self.G[v][a]["y"]
            cap=self.G[v][a]["cap"]
            rev=self.G[y][self.G[x][a]["rev"]]
            if self.used[y] or cap==0:continue
            f2=self.dfs(y,t,min(f,cap))
            if f2>0:
                self.G[v][a]["cap"]-=f2
                rev["cap"]+=f2
                return f2
        return 0
    def maxflow(self):
        flow=0
        while True:
            self.used=[False]*V
            zouka=self.dfs(self.s,self.t)
            if zouka==0:break
            flow+=zouka
        return flow



######################################################################################################
def f(A):
    ssum=sum(A)
    dp=[[0 for b in range(ssum+1)] for a in range(len(A)+1)]
    dp[0][0]=1
    for i in range(1,len(A)+1):
        for s in range(ssum+1):
            dp[i][s]+=dp[i-1][s]*2
            if s-A[i-1]>=0:
                dp[i][s]+=dp[i-1][s-A[i-1]]
            dp[i][s]%=998244353
    return dp
n,S=inputintlist()
A=inputintlist()
dp=f(A)
ans=dp[n][S]
print(ans)

Submission status: Runtime Error

Solution code:
import numpy as np
import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)
fft = np.fft.rfft
ifft = np.fft.irfft
mod = 998244353

N, S = map(int, input().split())
A = list(map(int, input().split()))
U = sum(A)

dp = np.zeros(U+10, dtype=np.int64)
dp[0] = 1
for a in A:
    newDP = dp.copy() * 2
    newDP[a:] += dp[:-a]
    newDP %= mod
    dp = newDP

print(dp[S])

Submission status: Runtime Error

Solution code:
import numpy as np
import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)
fft = np.fft.rfft
ifft = np.fft.irfft
mod = 998244353

N, S = map(int, input().split())
A = list(map(int, input().split()))
U = sum(A)

dp = np.zeros(U+10, dtype=np.int64)
dp[0] = 1
for a in A:
    newDP = dp.copy() * 2
    if a <= S:
        newDP[a:] += dp[:-a]
        newDP %= mod
    dp = newDP

print(dp[S])

Submission status: Runtime Error

Solution code:
# coding: utf-8
#import numpy as np
import re
import math
from collections import defaultdict
from collections import deque
import collections
from fractions import Fraction
import bisect
from queue import PriorityQueue
import itertools
from copy import deepcopy
import random
import time
import os
import sys
import datetime
from functools import lru_cache
from functools import reduce
readline=sys.stdin.readline
sys.setrecursionlimit(2000000)
alphabet="abcdefghijklmnopqrstuvwxyz"
numbers="0123456789"
mod=int(10**9+7)
inf=int(10**19)
class Edge():
    def __init__(self,x,y,val=1):
        self.x=x
        self.y=y
        self.val=val
class unionfind():
    def __init__(self,n):
        self.n=n
        self.P=[a for a in range(n)]
        self.rank=[0]*n
 
    def find(self,x):
        if(x!=self.P[x]):
            self.P[x]=self.find(self.P[x])
        return self.P[x]
 
    def same(self,x,y):
        return self.find(x)==self.find(y)
 
    def link(self,x,y):
        if self.rank[x]<self.rank[y]:
            self.P[x]=y
        elif self.rank[y]<self.rank[x]:
            self.P[y]=x
        else:
            self.P[x]=y
            self.rank[y]+=1
 
    def unite(self,x,y):
        self.link(self.find(x),self.find(y))
 
    def size(self):
        S=set()
        for a in range(self.n):
            S.add(self.find(a))
        return len(S)
def yn(b):
    if b:print("yes")
    else:print("no")
def Yn(b):
    if b:print("Yes")
    else:print("No")
def YN(b):
    if b:print("YES")
    else:print("NO")
def ispow(a,b):
    now=b
    while now<a:
        now*=b
    return now==a
def getbin(num,size):
    A=[0]*size
    for a in range(size):
        if (num>>(size-a-1))&1==1:
            A[a]=1
        else:
            A[a]=0
    return A
def getfacs(n,mod_=0):
    A=[1]*(n+1)
    for a in range(2,len(A)):
        A[a]=A[a-1]*a
        if(mod_>0):A[a]%=mod_
    return A
def comb(n,r,mod,fac):
    if(n-r<0):return 0
    return (fac[n]*pow(fac[n-r],mod-2,mod)*pow(fac[r],mod-2,mod))%mod
def nextcomb(num,size):
    x=num&(-num)
    y=num+x
    z=num&(~y)
    z//=x
    z=z>>1
    num=(y|z)
    if(num>=(1<<size)):return False
    else:return num
def getprimes(n):
    if n==0:return []
    A=[True]*(n+1)
    A[0]=False
    A[1]=False
    for a in range(2,n+1):
        if A[a]:
            for b in range(a*2,n+1,a):
                A[b]=False
    ret=[]
    for a in range(n+1):
        if(A[a]):ret.append(a)
    return ret
def isprime(num):
    if(num<=1):return False
    i=2
    while i*i<=num:
       if(num%i==0):return False
       i+=1
    return True
def ifelse(bbool,ret1,ret2):
    if bbool:return ret1
    else:return  ret2
def join(A,c=" "):
    n=len(A)
    A=list(map(str,A))
    s=""
    for a in range(n):
        s+=A[a]
        if(a<n-1):s+=c
    return s
def factorize(n):
    b = 2
    ret=defaultdict(int)
    while b * b <= n:
        while n % b == 0:
            n //= b
            ret[b]+=1
        b+=1
    if n > 1:ret[n]+=1
    return ret
def pm(x):
    return x//abs(x)
def inputintlist(): 
    return list(map(int,input().split()))
def inputfloatlist(): 
    return list(map(float,input().split()))
def tozero(A):
    ret=[None]*len(A)
    for a in range(len(A)):
        ret[a]=A[a]-1
    return ret
def istanchouzouka(A):
    f=True
    prev=min(A)-1
    for a in A:
        if prev>=a:
            f=False
        prev=a
    return f
def istanchouhigensyou(A):
    f=True
    prev=min(A)-1
    for a in A:
        if prev>a:
            f=False
        prev=a
    return f
def getallsum(A):
    s=sum(A)
    dp=defaultdict(int)
    dp[0]=1
    for a in range(0,len(A)):
        for b in range(s,-1,-1):
            if b-A[a]>=0:
                dp[b]+=dp[b-A[a]]
    return dp
def yuukoutomukou(edges):
    ret=deepcopy(edges)
    for edge in edges:
        if not edge.x==edge.y:
            ret.append(Edge(edge.y,edge.x,edge.val))
    return ret
def dijkstra(edges,V,start):
    mincost=[inf]*V
    G=[[] for a in range(V)]
    for edge in edges:
        G[edge.x].append([edge.val,edge.y])
    Q=PriorityQueue()
    Q.put([0,start])#[cost,x]
    while not Q.empty():
        nowcost,nowx=Q.get()
        if mincost[nowx]==inf:
            mincost[nowx]=nowcost
            for cost,y in G[nowx]:
                newcost=nowcost+cost
                Q.put([newcost,y])
    return mincost
def warshallfloyd(edges,V):
    mincost=[[inf for b in range(V)] for a in range(V)]
    for a in range(V):mincost[a][a]=0
    for edge in edges:
        mincost[edge.x][edge.y]=min(mincost[edge.x][edge.y],edge.val)#x→yが複数ある場合のためにmin()する
    for k in range(V):
        for s in range(V):
            for t in range(V):
                if mincost[s][k]==inf or mincost[k][t]==inf:continue
                mincost[s][t]=min(mincost[s][t],mincost[s][k]+mincost[k][t])
    return mincost
def bellemanford(edges,V,start):
    mincost=[inf]*V
    mincost[start]=0
    for _ in range(V):
        for edge in edges:
            if mincost[edge.x]==inf:continue
            mincost[edge.y]=min(mincost[edge.y],mincost[edge.x]+edge.val)
    return mincost
def ruisekiwa(A):
    ret=[0]*(len(A)+1)
    for a in range(len(A)):
        ret[a+1]=ret[a]+A[a]
    return ret
def getmd(x1,y1,x2,y2):
    return abs(x1-x2)+abs(y1-y2)
def geted(x1,y1,x2,y2):
    return math.sqrt((x1-x2)**2+(y1-y2)**2)
class fordfulkerson():
    def __init__(self,edges,V,s,t):
        self.V=V
        self.used=[False]*V
        self.G=[[] for a in range(V)]
        self.s=s
        self.t=t
        for edge in edges:
            self.G[edge.x].append({"x":edge.x,"y":edge.y,"cap":edge.val,"rev":len(self.G[edge.y])})
            self.G[edge.y].append({"x":edge.y,"y":edge.x,"cap":0,"rev":len(self.G[edge.x])-1})
    def dfs(self,v,t,f=inf):
        if v==t:return f
        self.used[v]=True
        for a in range(len(self.G[v])):
            x=self.G[v][a]["x"]
            y=self.G[v][a]["y"]
            cap=self.G[v][a]["cap"]
            rev=self.G[y][self.G[x][a]["rev"]]
            if self.used[y] or cap==0:continue
            f2=self.dfs(y,t,min(f,cap))
            if f2>0:
                self.G[v][a]["cap"]-=f2
                rev["cap"]+=f2
                return f2
        return 0
    def maxflow(self):
        flow=0
        while True:
            self.used=[False]*V
            zouka=self.dfs(self.s,self.t)
            if zouka==0:break
            flow+=zouka
        return flow



######################################################################################################
def f(A):
    ssum=sum(A)
    dp=[[0 for b in range(ssum+1)] for a in range(len(A)+1)]
    dp[0][0]=1
    for i in range(1,len(A)+1):
        for s in range(ssum+1):
            dp[i][s]=dp[i-1][s]
            dp[i][s]%=998244353
            if s-A[i-1]>=0:
                dp[i][s]+=dp[i-1][s-A[i-1]]
            dp[i][s]%=998244353
    return dp
n,S=inputintlist()
A=inputintlist()
dp=f(A)
ans=dp[-1][S]
print(ans)

Submission status: Runtime Error

Solution code:
def resolve():
    n, s = map(int, input().split())
    a = list(map(int, input().split()))
    mod = 998244353
    dp = [0] * (s + 1)
    dp[0] = 1
    for i in a:
        for j in range(s - i, -1, -1):
            dp[j + i] = dp[j + i] * 2 + dp[j]
            dp[j + i] %= mod
        for j in range(min(i, s + 2)):
            dp[j] *= 2
            dp[j] %= mod
    print(dp[-1])


if __name__ == '__main__':
    resolve()

Submission status: Runtime Error

Solution code:
def resolve():
    n, s = map(int, input().split())
    a = list(map(int, input().split()))
    mod = 998244353
    dp = [0] * (s + 1)
    dp[0] = 1
    for i in a:
        for j in range(s - i, -1, -1):
            dp[j + i] = dp[j + i] * 2 + dp[j]
            dp[j + i] %= mod
        for j in range(i):
            dp[j] *= 2
            dp[j] %= mod
    print(dp[-1])


if __name__ == '__main__':
    resolve()

Submission status: Runtime Error

Solution code:
# coding: utf-8
#import numpy as np
import re
import math
from collections import defaultdict
from collections import deque
import collections
from fractions import Fraction
import bisect
from queue import PriorityQueue
import itertools
from copy import deepcopy
import random
import time
import os
import sys
import datetime
from functools import lru_cache
from functools import reduce
readline=sys.stdin.readline
sys.setrecursionlimit(2000000)
alphabet="abcdefghijklmnopqrstuvwxyz"
numbers="0123456789"
mod=int(10**9+7)
inf=int(10**19)
class Edge():
    def __init__(self,x,y,val=1):
        self.x=x
        self.y=y
        self.val=val
class unionfind():
    def __init__(self,n):
        self.n=n
        self.P=[a for a in range(n)]
        self.rank=[0]*n
 
    def find(self,x):
        if(x!=self.P[x]):
            self.P[x]=self.find(self.P[x])
        return self.P[x]
 
    def same(self,x,y):
        return self.find(x)==self.find(y)
 
    def link(self,x,y):
        if self.rank[x]<self.rank[y]:
            self.P[x]=y
        elif self.rank[y]<self.rank[x]:
            self.P[y]=x
        else:
            self.P[x]=y
            self.rank[y]+=1
 
    def unite(self,x,y):
        self.link(self.find(x),self.find(y))
 
    def size(self):
        S=set()
        for a in range(self.n):
            S.add(self.find(a))
        return len(S)
def yn(b):
    if b:print("yes")
    else:print("no")
def Yn(b):
    if b:print("Yes")
    else:print("No")
def YN(b):
    if b:print("YES")
    else:print("NO")
def ispow(a,b):
    now=b
    while now<a:
        now*=b
    return now==a
def getbin(num,size):
    A=[0]*size
    for a in range(size):
        if (num>>(size-a-1))&1==1:
            A[a]=1
        else:
            A[a]=0
    return A
def getfacs(n,mod_=0):
    A=[1]*(n+1)
    for a in range(2,len(A)):
        A[a]=A[a-1]*a
        if(mod_>0):A[a]%=mod_
    return A
def comb(n,r,mod,fac):
    if(n-r<0):return 0
    return (fac[n]*pow(fac[n-r],mod-2,mod)*pow(fac[r],mod-2,mod))%mod
def nextcomb(num,size):
    x=num&(-num)
    y=num+x
    z=num&(~y)
    z//=x
    z=z>>1
    num=(y|z)
    if(num>=(1<<size)):return False
    else:return num
def getprimes(n):
    if n==0:return []
    A=[True]*(n+1)
    A[0]=False
    A[1]=False
    for a in range(2,n+1):
        if A[a]:
            for b in range(a*2,n+1,a):
                A[b]=False
    ret=[]
    for a in range(n+1):
        if(A[a]):ret.append(a)
    return ret
def isprime(num):
    if(num<=1):return False
    i=2
    while i*i<=num:
       if(num%i==0):return False
       i+=1
    return True
def ifelse(bbool,ret1,ret2):
    if bbool:return ret1
    else:return  ret2
def join(A,c=" "):
    n=len(A)
    A=list(map(str,A))
    s=""
    for a in range(n):
        s+=A[a]
        if(a<n-1):s+=c
    return s
def factorize(n):
    b = 2
    ret=defaultdict(int)
    while b * b <= n:
        while n % b == 0:
            n //= b
            ret[b]+=1
        b+=1
    if n > 1:ret[n]+=1
    return ret
def pm(x):
    return x//abs(x)
def inputintlist(): 
    return list(map(int,input().split()))
def inputfloatlist(): 
    return list(map(float,input().split()))
def tozero(A):
    ret=[None]*len(A)
    for a in range(len(A)):
        ret[a]=A[a]-1
    return ret
def istanchouzouka(A):
    f=True
    prev=min(A)-1
    for a in A:
        if prev>=a:
            f=False
        prev=a
    return f
def istanchouhigensyou(A):
    f=True
    prev=min(A)-1
    for a in A:
        if prev>a:
            f=False
        prev=a
    return f
def getallsum(A):
    s=sum(A)
    dp=defaultdict(int)
    dp[0]=1
    for a in range(0,len(A)):
        for b in range(s,-1,-1):
            if b-A[a]>=0:
                dp[b]+=dp[b-A[a]]
    return dp
def yuukoutomukou(edges):
    ret=deepcopy(edges)
    for edge in edges:
        if not edge.x==edge.y:
            ret.append(Edge(edge.y,edge.x,edge.val))
    return ret
def dijkstra(edges,V,start):
    mincost=[inf]*V
    G=[[] for a in range(V)]
    for edge in edges:
        G[edge.x].append([edge.val,edge.y])
    Q=PriorityQueue()
    Q.put([0,start])#[cost,x]
    while not Q.empty():
        nowcost,nowx=Q.get()
        if mincost[nowx]==inf:
            mincost[nowx]=nowcost
            for cost,y in G[nowx]:
                newcost=nowcost+cost
                Q.put([newcost,y])
    return mincost
def warshallfloyd(edges,V):
    mincost=[[inf for b in range(V)] for a in range(V)]
    for a in range(V):mincost[a][a]=0
    for edge in edges:
        mincost[edge.x][edge.y]=min(mincost[edge.x][edge.y],edge.val)#x→yが複数ある場合のためにmin()する
    for k in range(V):
        for s in range(V):
            for t in range(V):
                if mincost[s][k]==inf or mincost[k][t]==inf:continue
                mincost[s][t]=min(mincost[s][t],mincost[s][k]+mincost[k][t])
    return mincost
def bellemanford(edges,V,start):
    mincost=[inf]*V
    mincost[start]=0
    for _ in range(V):
        for edge in edges:
            if mincost[edge.x]==inf:continue
            mincost[edge.y]=min(mincost[edge.y],mincost[edge.x]+edge.val)
    return mincost
def ruisekiwa(A):
    ret=[0]*(len(A)+1)
    for a in range(len(A)):
        ret[a+1]=ret[a]+A[a]
    return ret
def getmd(x1,y1,x2,y2):
    return abs(x1-x2)+abs(y1-y2)
def geted(x1,y1,x2,y2):
    return math.sqrt((x1-x2)**2+(y1-y2)**2)
class fordfulkerson():
    def __init__(self,edges,V,s,t):
        self.V=V
        self.used=[False]*V
        self.G=[[] for a in range(V)]
        self.s=s
        self.t=t
        for edge in edges:
            self.G[edge.x].append({"x":edge.x,"y":edge.y,"cap":edge.val,"rev":len(self.G[edge.y])})
            self.G[edge.y].append({"x":edge.y,"y":edge.x,"cap":0,"rev":len(self.G[edge.x])-1})
    def dfs(self,v,t,f=inf):
        if v==t:return f
        self.used[v]=True
        for a in range(len(self.G[v])):
            x=self.G[v][a]["x"]
            y=self.G[v][a]["y"]
            cap=self.G[v][a]["cap"]
            rev=self.G[y][self.G[x][a]["rev"]]
            if self.used[y] or cap==0:continue
            f2=self.dfs(y,t,min(f,cap))
            if f2>0:
                self.G[v][a]["cap"]-=f2
                rev["cap"]+=f2
                return f2
        return 0
    def maxflow(self):
        flow=0
        while True:
            self.used=[False]*V
            zouka=self.dfs(self.s,self.t)
            if zouka==0:break
            flow+=zouka
        return flow



######################################################################################################
def f(A):
    ssum=sum(A)
    dp=[[0 for b in range(ssum+1)] for a in range(len(A)+1)]
    dp[0][0]=1
    for i in range(1,len(A)+1):
        for s in range(ssum+1):
            dp[i][s]=dp[i-1][s]*2
            if s-A[i-1]>=0:
                dp[i][s]+=dp[i-1][s-A[i-1]]
            dp[i][s]%=998244353
    return dp
n,S=inputintlist()
A=inputintlist()
dp=f(A)
ans=dp[-1][S]
print(ans)