qyliang/CodeNanoFix huggingface dataset:
Buggy code:
def lp(node,memo,graph):
    if memo[node] != -1:
        return memo[node]
    cand = [0]
    if graph[node]:
        for neighbor in graph[node]:
            cand.append(lp(neighbor,memo,graph))
        maximam = max(cand)+1
    else:
        maximam = 0
    memo[node]=maximam
    return maximam

import sys
sys.setrecursionlimit(10**10)
N,M = map(int, input().split())
graph = {}
for i in range(N+1):
    graph[i] = []
for _ in range(M):
    x,y = map(int,input().split())
    graph[x].append(y)
ans = 0
memo = [-1]*(N+1)
for i in range(1,N+1):
    ans = max(ans, lp(i,memo,graph))
print(ans)

Fixed code:
def lp(node,memo,graph):
    if memo[node] != -1:
        return memo[node]
    cand = [0]
    if graph[node]:
        for neighbor in graph[node]:
            cand.append(lp(neighbor,memo,graph))
        maximam = max(cand)+1
    else:
        maximam = 0
    memo[node]=maximam
    return maximam

import sys
sys.setrecursionlimit(10**5)
N,M = map(int, input().split())
graph = {}
for i in range(N+1):
    graph[i] = []
for _ in range(M):
    x,y = map(int,input().split())
    graph[x].append(y)
ans = 0
memo = [-1]*(N+1)
for i in range(1,N+1):
    ans = max(ans, lp(i,memo,graph))
print(ans)
Buggy code:
from heapq import heappush, heappop
import collections
import math
import heapq
from collections import defaultdict
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
MOD = 10 ** 9 + 7
inf = float("inf")


def main():
    n, m = map(int, input().split())
    e = [[]for i in range(n)]
    for i in range(m):
        a, b = map(int, input().split())
        a -= 1
        b -= 1
        e[a].append(b)

    dp = [-1 for i in range(n)]
    def f(i):
        if dp[i] != -1:
            return dp[i]
        ret = 0
        for v in e[i]:
            ret = max(ret, f(v) + 1)
        dp[i] = ret
        return dp[i]

    ans = 0
    for i in range(n):
        ans = max(f(i), ans)
    print(ans, dp)


if __name__ == '__main__':
    main()


Fixed code:
from heapq import heappush, heappop
import collections
import math
import heapq
from collections import defaultdict
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
MOD = 10 ** 9 + 7
inf = float("inf")


def main():
    n, m = map(int, input().split())
    e = [[]for i in range(n)]
    for i in range(m):
        a, b = map(int, input().split())
        a -= 1
        b -= 1
        e[a].append(b)

    dp = [-1 for i in range(n)]
    vis = [False for i in range(n)]

    def f(i):
        if vis[i]:
            return dp[i]
        ret = 0
        for v in e[i]:
            ret = max(ret, f(v) + 1)
        vis[i] = True
        dp[i] = ret
        return dp[i]

    ans = 0
    for i in range(n):
        ans = max(f(i), ans)
    print(ans)


if __name__ == '__main__':
    main()
Buggy code:
import sys

sys.setrecursionlimit(10 ** 5 * 2)
input = sys.stdin.readline()
N, M = map(int, input().split())
Ps = [[] for _ in range(N)]
for i in range(M):
    x, y = map(int, input().split())
    Ps[x - 1].append(y - 1)

mem = [-1] * N


def rec(n):
    if mem[n] > -1:
        return mem[n]
    elif len(Ps[n]) == 0:
        mem[n] = 0
        return mem[n]
    else:
        mem[n] = max([rec(Ps[n][i]) for i in range(len(Ps[n]))]) + 1
        return mem[n]


for i in range(N):
    rec(i)
print(max(mem))

Fixed code:
import sys

sys.setrecursionlimit(10 ** 5 * 2)
N, M = map(int, input().split())
Ps = [[] for _ in range(N)]
for i in range(M):
    x, y = map(int, input().split())
    Ps[x - 1].append(y - 1)

mem = [-1] * N


def rec(n):
    if mem[n] > -1:
        return mem[n]
    elif len(Ps[n]) == 0:
        mem[n] = 0
        return mem[n]
    else:
        mem[n] = max([rec(Ps[n][i]) for i in range(len(Ps[n]))]) + 1
        return mem[n]


for i in range(N):
    rec(i)
print(max(mem))
Buggy code:
from collections import defaultdict
import sys
sys.setrecursionlimit(10**10)
N,M = map(int,input().split())

d = defaultdict(lambda:[])

for _ in range(M):
    x,y = map(int,input().split())
    x -= 1
    y -= 1
    d[x].append(y)

dp = [-1]*N

def dist(s):
    if dp[s] >= 0:
        return dp[s]
    if d[s] == []:
        dp[s] = 0
        return 0
    res = 0
    for t in d[s]:
        res = max(res,1+dist(t))
    dp[s] = res
    return res

ans = 0
for i in range(N):
    ans = max(ans,dist(i))

print(ans)

Fixed code:
from collections import defaultdict
import sys
sys.setrecursionlimit(10**9)
N,M = map(int,input().split())

d = defaultdict(lambda:[])

for _ in range(M):
    x,y = map(int,input().split())
    x -= 1
    y -= 1
    d[x].append(y)

dp = [-1]*N

def dist(s):
    if dp[s] >= 0:
        return dp[s]
    if d[s] == []:
        dp[s] = 0
        return 0
    res = 0
    for t in d[s]:
        res = max(res,1+dist(t))
    dp[s] = res
    return res

ans = 0
for i in range(N):
    ans = max(ans,dist(i))

print(ans)
Buggy code:
n , m = map(int, input().split())
edge=[[] for _ in range(n)]
deg=[0] * n
for i in range(m):
    x, y =map(int, input().split())
    edge[x - 1 ].append(y - 1)
    deg[y - 1] +=1 

from collections import deque

que =deque()
for i in range(n):
    if deg[i] == 0:
        que.append(i)
dp = [0] *n

while que:
    v = que.popleft()
    nv = edge[v]
    for nv in nv:
        deg[nv] -=1
        if deg[nv] ==0:
            que.append(nv)
            dp[nv] = max(dp[v] + 1 ,dp[nv])
print(max(dp)

Fixed code:
n , m = map(int, input().split())
edge=[[] for _ in range(n)]
deg=[0] * n
for i in range(m):
    x, y =map(int, input().split())
    edge[x - 1 ].append(y - 1)
    deg[y - 1] +=1 

from collections import deque

que =deque()
for i in range(n):
    if deg[i] == 0:
        que.append(i)
dp = [0] *n

while que:
    v = que.popleft()
    nv = edge[v]
    for nv in nv:
        deg[nv] -=1
        if deg[nv] ==0:
            que.append(nv)
            dp[nv] = max(dp[v] + 1 ,dp[nv])
print(max(dp))
Buggy code:
from collections import defaultdict, deque
def sub():

    N, M = [int(e) for e in input().split()]
    es = [[int(x) for x in input().split()] for _ in range(N)]

    outs = defaultdict(list)
    ins = defaultdict(int)
    for v1, v2 in es:
        outs[v1].append(v2)
        ins[v2] += 1

    q = deque(v1 for v1 in range(v) if ins[v1] == 0)
    dp_table = [0 for i in range(N+1)]
    res = []
    while q:
        v1 = q.popleft()
        res.append(v1)
        for v2 in outs[v1]:
            ins[v2] -= 1
            if ins[v2] == 0:
                q.append(v2)
                dp_table[v2] = max(dp_table[v2], dp_table[v1] + 1)
    print(max(dp_table))

if __name__ == "__main__":
    sub()


Fixed code:
from collections import defaultdict, deque
def sub():

    N, M = [int(e) for e in input().split()]
    es = [[int(x) for x in input().split()] for _ in range(M)]

    outs = defaultdict(list)
    ins = defaultdict(int)
    for v1, v2 in es:
        outs[v1].append(v2)
        ins[v2] += 1

    q = deque(v1 for v1 in range(1, N+1) if ins[v1] == 0)
    dp_table = [0 for i in range(N+1)]
    res = []
    while q:
        v1 = q.popleft()
        res.append(v1)
        for v2 in outs[v1]:
            ins[v2] -= 1
            if ins[v2] == 0:
                q.append(v2)
                dp_table[v2] = max(dp_table[v2], dp_table[v1] + 1)
    print(max(dp_table))

if __name__ == "__main__":
    sub()
Buggy code:
from collections import defaultdict
from functools import lru_cache
import sys
sys.setrecursionlimit(1000000)


N, M = map(int, input().split())
XY = [map(int, input().split()) for _ in range(M)]

dp = [-1 for _ in range(N + 1)]

x_to_y = defaultdict(list)
for x, y in XY:
    x_to_y[x].append(y)


@lru_cache(N)
def depth(n):
    ret = -1
    for y in x_to_y[n]:
        ret = max(ret, depth(y))
    return ret + 1


        
depths = [depth(n) for n in range(1, N + 1)]
print(max(depths), default=0)


Fixed code:
from collections import defaultdict
from functools import lru_cache
import sys
sys.setrecursionlimit(1000000)


N, M = map(int, input().split())
XY = [map(int, input().split()) for _ in range(M)]

dp = [-1 for _ in range(N + 1)]

x_to_y = defaultdict(list)
for x, y in XY:
    x_to_y[x].append(y)


@lru_cache(N)
def depth(n):
    ret = -1
    for y in x_to_y[n]:
        ret = max(ret, depth(y))
    return ret + 1


        
depths = [depth(n) for n in range(1, N + 1)]
print(max(depths))
Buggy code:
# coding: utf-8
from functools import lru_cache
sys.setrecursionlimit(10000)

import sys
input = sys.stdin.readline

@lru_cache(maxsize = None)
def f(v):
    if len(arc[v]) == 0:
        return(0)
    return(max(f(nv) for nv in arc[v]) + 1)

n, m = map(int, input().split()) # 2 <= n <= 10^5, 1 <= m <= 10^5
arc = [[] for _ in range(n + 1)]
for i in range(m):
    x, y = map(int, input().split())
    arc[x].append(y)
print(max(f(v + 1) for v in range(n)))


Fixed code:
# coding: utf-8
from functools import lru_cache

import sys
input = sys.stdin.readline
sys.setrecursionlimit(1000000)

@lru_cache(maxsize = None)
def f(v):
    if not arc[v]:
        return(0)
    return(max(f(nv) for nv in arc[v]) + 1)

n, m = map(int, input().split()) # 2 <= n <= 10^5, 1 <= m <= 10^5
arc = [[] for _ in range(n)]
for _ in range(m):
    x, y = map(int, input().split())
    arc[x - 1].append(y - 1)
print(max(f(v) for v in range(n)))
Buggy code:
N, M = (int(i) for i in input().split()) 
 
outs = [[] for i in range(N)]
ins = [0] * N
 
for _ in range(M):
    x, y = (int(i) for i in input().split())
    x -= 1
    y -= 1
    outs[x].append(y)
    ins[y] += 1
 
q = []
for i in range(N):
    if ins[i] == 0:
        q.append(i)
 
last = [0] * N
while q != []:
    qn = q.poplef()
    for v in outs[qn]:
        ins[v] -= 1
        last[v] = max(last[v], last[qn] + 1)
        if ins[v] == 0:
            q.append(v)
 
print(max(last))

Fixed code:
N, M = (int(i) for i in input().split()) 

outs = [[] for i in range(N)]
ins = [0] * N

for _ in range(M):
    x, y = (int(i) for i in input().split())
    x -= 1
    y -= 1
    outs[x].append(y)
    ins[y] += 1

q = []
for i in range(N):
    if ins[i] == 0:
        q.append(i)

last = [0] * N
while q != []:
    qn = q.pop()
    for v in outs[qn]:
        ins[v] -= 1
        last[v] = max(last[v], last[qn] + 1)
        if ins[v] == 0:
            q.append(v)

print(max(last))
Buggy code:
N,M = map(int,input().split())
L = [list(map(int,input().split())) for i in range(M)]

L_minus = [[] for i in range(N)]
L_plus = [0 for i in range(N)]

dp = [0 for i in range(N)]

for i in range(M) :
    x,y = L[i]
    x -= 1
    y -= 1
    L_plus[y] += 1
    L_minus[x].append(y)

A = []

for i in range(N) :
    if L_plus[i] == 0 :
        A.append(i)

while A :
    x = A.popleft()
    
    for y in L_minus[x] :
        L_plus[y] -= 1
        if L_plus[y] == 0 :
            A.append(y)
        dp[y] = max(dp[y], dp[x]+1)

ans = max(dp)

print(ans)

Fixed code:
N,M = map(int,input().split())
L = [list(map(int,input().split())) for i in range(M)]

L_minus = [[] for i in range(N)]
L_plus = [0 for i in range(N)]

dp = [0 for i in range(N)]

for i in range(M) :
    x,y = L[i]
    x -= 1
    y -= 1
    L_plus[y] += 1
    L_minus[x].append(y)

A = []

for i in range(N) :
    if L_plus[i] == 0 :
        A.append(i)

while A :
    x = A.pop()
    
    for y in L_minus[x] :
        L_plus[y] -= 1
        if L_plus[y] == 0 :
            A.append(y)
        dp[y] = max(dp[y], dp[x]+1)

ans = max(dp)

print(ans)
Buggy code:
from sys import stdin
input = stdin.readline
N, M = map(int, input().split())
# d = [0] * (N + 1)
adj = [[] for _ in range(N + 1)]
for _ in range(M):
    x, y = map(int, input().split())
    adj[x].append(y)
    # d[y] += 1

dp = [-1] * (N + 1)


def lp(x: 'int') -> 'int':
    if dp[x] >= 0:
        return dp[x]
    else:
        dp[x] = 0
        for y in adj[x]:
            dp[x] = max(dp[x], lp(y) + 1)
        return dp[x]


print(max(lp(i) for i in range(1, N)))


Fixed code:
from sys import stdin, setrecursionlimit
# input = stdin.readline
setrecursionlimit(200000)
N, M = map(int, input().split())
# d = [0] * (N + 1)
adj = [[] for _ in range(N + 1)]
for _ in range(M):
    x, y = map(int, input().split())
    adj[x].append(y)
    # d[y] += 1

dp = [-1] * (N + 1)


def lp(x: 'int') -> 'int':
    if dp[x] >= 0:
        return dp[x]
    else:
        dp[x] = 0
        for y in adj[x]:
            dp[x] = max(dp[x], lp(y) + 1)
        return dp[x]


print(max(lp(i) for i in range(1, N + 1)))
Buggy code:
n, k = map(int, input().split())
a = list(map(int, input().split()))

dp = [0] * (k+1)

for i in range(1, k+1):
    for j in range(n):
        if i - a[j] >= 0 and dp[i-a[j]] == 0:
            dp[i] = 1

print(dp[k])

Fixed code:
n,k = map(int,input().split())
a = list(map(int,input().split()))
dp = ['Second'] * (k+1)
for i in range(1,k+1):
    for j in range(1,n+1):
        if i-a[j-1] >= 0 and dp[i-a[j-1]] == 'Second':
            dp[i] = 'First'
print(dp[k])
Buggy code:
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop,heapify
import math
from collections import *
from functools import reduce,cmp_to_key
import sys
input = sys.stdin.readline

from itertools import accumulate
from functools import lru_cache

M = mod = 998244353
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
 
def li():return [int(i) for i in input().rstrip('\n').split()]
def st():return input().rstrip('\n')
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input().rstrip('\n')]
def li3():return [int(i) for i in input().rstrip('\n')]



n, k = li()
l = li()

dp = [False] * (k + 1)

for i in l:
    for j in range(k + 1):
        if not dp[j - i] and j <= i:dp[j] = True

print('First' if dp[k] else 'Second')

Fixed code:
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop,heapify
import math
from collections import *
from functools import reduce,cmp_to_key
import sys
input = sys.stdin.readline

from itertools import accumulate
from functools import lru_cache

M = mod = 998244353
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
 
def li():return [int(i) for i in input().rstrip('\n').split()]
def st():return input().rstrip('\n')
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input().rstrip('\n')]
def li3():return [int(i) for i in input().rstrip('\n')]



n, k = li()
l = li()

dp = [False] * (k + 1)


for j in range(k + 1):
    for i in l:
        if j >= i and not dp[j - i]:dp[j] = True

print('First' if dp[k] else 'Second')
Buggy code:
n, k = map(int, input().strip().split())
arr = list(map(int, input().strip().split()))

dp = [0 for i in range(k+1)]
for i in range(len(dp)):
    for j in arr:
        if j+i < k+1:
            dp[j+i] = (dp[i]+1)%2

ans = "First" if dp[-1] else "Second"
print(ans)



Fixed code:
n, k = map(int, input().strip().split())
arr = list(map(int, input().strip().split()))

dp = [0 for i in range(k+1)]

for i in range(len(dp)):
    if dp[i] == 0:
        for j in arr:
            if j+i < k+1:
                dp[j+i] = 1

ans = "First" if dp[-1] else "Second"
print(ans)
Buggy code:
n, k = map(int, input().split())
a_list = list(map(int, input().split()))
dp = [False]*(k+1)

for i in range(k):
  for j in range(n):
    if i-a_list[j] >= 0:
      dp[i] |= not(dp[i-a_list[j]])
      
if dp[k-1]:
  print('First')
else:
  print('Second')

Fixed code:
n,k=map(int,input().split())
a=list(map(int,input().split()))
dp=[False]*(k+1)
for i in range(1,k+1):
  for j in range(n):
    if i-a[j]>=0:
      dp[i] |= not(dp[i-a[j]])
#print(dp)
print("First" if dp[k] else "Second")
Buggy code:
N, K  = map(int,input().split())
A = list(map(int,input().split()))

dp = [None for _ in range(K+1)]
dp[0] = 0
for k in range(1,K+1):
	for a in A:
		if k-a>=0:
			if dp[k-a]==0:
				dp[k]=1


if dp[K]==1:
	print('First')
else:
	print('Second')

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

dp = [0 for _ in range(K+1)]
dp[0] = 0
for k in range(1,K+1):
	for a in A:
		if k-a>=0:
			if dp[k-a]==0:
				dp[k]=1


if dp[K]==1:
	print('First')
else:
	print('Second')
Buggy code:
n,k = map(int,input().split())
a = []
for i in range(n):
  a.append(int(input()))

dp = [False]*(k+1)
dp[0] = 0

for i in range(1,k+1):
  for j in range(n):
    if i-a[j] >= 0 and dp[i-a[j]] == 0:
      dp[i] = 1
      break
    #dp[i] = 0

if dp[k] == 1:
  print("First")
else:
  print("Second")

Fixed code:
n,k = map(int,input().split())
a = [int(i) for i in input().split()]

dp = [0]*(k+1)
dp[0] = 0

for i in range(1,k+1):
  for j in range(n):
    if i-a[j] >= 0 and dp[i-a[j]] == 0:
      dp[i] = 1
      break
    #dp[i] = 0

if dp[k] == 1:
  print("First")
else:
  print("Second")
Buggy code:
import sys
def main():
    N,K=tuple(map(int,sys.stdin.readline().split()))
    a=tuple(map(int,sys.stdin.readline().split()))
    dp=[False for _ in range(K+1)]
    for i in range(K+1):
        for x in a:
            if i-x>=0:dp[i]=not dp[i-x]
    print('First') if dp[K] is True else print('Second')
if __name__=='__main__':main()

Fixed code:
import sys
def main():
    N,K=tuple(map(int,sys.stdin.readline().split()))
    a=tuple(map(int,sys.stdin.readline().split()))
    dp=[False for _ in range(K+1)]
    for i in range(K+1):
        for x in a:
            if i-x>=0:dp[i]=dp[i] or (not dp[i-x])
    print('First') if dp[K] is True else print('Second')
if __name__=='__main__':main()
Buggy code:
n, k = map(int, input().split())
a = list(map(int, input().split()))

dp = [False]*(k+1)

for i in range(k+1):
    flag = 0
    for j in a:
        if i-j < 0:
            continue
        if not dp[i-j]:
            flag = 1
            break

    if flag:
        dp[i] = True

if dp[k]:
    print("First")
else:
    print("Second")

print(dp)


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

dp = [False]*(k+1)

for i in range(k+1):
    flag = 0
    for j in a:
        if i-j < 0:
            continue
        if not dp[i-j]:
            flag = 1
            break

    if flag:
        dp[i] = True

if dp[k]:
    print("First")
else:
    print("Second")
Buggy code:
n,k=map(int,input().split())
arr=[int(i) for i in input().split()]
dp=[[0 for i in range(k+1)] for j in range(n+1)]
for i in range(1,n+1):
    for j in range(1,k+1):
        if arr[i-1]<=j:
            dp[i][j]=max(1^dp[i-1][j-arr[i-1]],dp[i-1][j])
        else:
            dp[i][j]=dp[i-1][j]
if dp[n][k]==1:
    print("First")
else:
    print("Second")


Fixed code:
n,k=map(int,input().split())
arr=[int(i) for i in input().split()]
dp=[0 for i in range(k+1)]
for i in range(1,k+1):
    for j in range(n):
        if arr[j]<=i and dp[i-arr[j]]==0:
            dp[i]=1
if dp[k]==1:
    print("First")
else:
    print("Second")
Buggy code:
n,k=map(int,input().split())
li=[int(k) for k in input().split()]
dp=[False]*(n+1)
for i in range(1,k+1):
  for j in range(len(li)):
    if i-li[j]<0:
      dp[i]=False
    else:
      if dp[i-li[j]]==False:
        dp[i]=True
if dp[k]==True:
  print("First")
else:
  print("Second")
  
  

Fixed code:
n,k=map(int,input().split())
li=[int(k) for k in input().split()]
dp=[False]*(k+1)
for i in range(1,k+1):
  for j in range(len(li)):
    if i-li[j]<0:
      continue
    if dp[i-li[j]]==False:
      dp[i]=True
      break
if dp[k]==True:
  print("First")
else:
  print("Second")
Buggy code:
n, k = map(int, input().split())
a = list(map(int, input().split()))

dp = [1] * k
player = ["Second", "First"]

for i in range(k):
    for j in range(n):
        if 0 <= i - a[j] and dp[i - a[j]] == 1:
            dp[i] = 0

print(player[dp[k - 1]])

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

dp = [1] * (k + 1)
player = ["First", "Second"]

for i in range(1, k + 1):
    for j in range(n):
        if 0 <= i - a[j] and dp[i - a[j]] == 1:
            dp[i] = 0

print(player[dp[k]])
Buggy code:
from sys import stdin,stdout
n,k=map(int,stdin.readline().split())
a=list(map(int,stdin.readline().split()))
dp=[[-1,-1] for i in range(k+1)]
for i in range(1,k+1):
    for j in a:
        if i>=j:
            if dp[i-j][0]==-1 and dp[i-j][1]==-1:
                dp[i][0]=1
            if dp[i-j][0]==1:
                dp[i][1]=1 
            if dp[i-j][1]==1:
                dp[i][0]=1
if dp[k][0]==1:
    print('First')
else:
    print('Second')
                

Fixed code:
from sys import stdin,stdout
n,k=map(int,stdin.readline().split())
a=list(map(int,stdin.readline().split()))
dp=[[-1,-1] for i in range(k+1)]
for i in range(1,k+1):
    for j in a:
        if i>=j:
            if dp[i-j][0]==-1 and dp[i-j][1]==-1:
                dp[i][0]=1
            elif dp[i-j][1]==1:
                dp[i][0]=1
    if dp[i][0]==-1:
        dp[i][1]=1
if dp[k][0]==1:
    print('First')
else:
    print('Second')
# print(dp)
Buggy code:
import sys
input = sys.stdin.readline

n, k = map(int, input().split())
A = list(map(int, input().split()))
dp = [0]*(k+1)
for i in range(k+1):
  for a in A:
    if i-a >= 0 and ~dp[i-a]:
      dp[i] = 1
      break
result = dp[k]
if result:
  print("First")
else:
  print("Second")

Fixed code:
import sys
input = sys.stdin.readline

n, k = map(int, input().split())
A = list(map(int, input().split()))
dp = [0]*(k+1)
for i in range(k+1):
  for a in A:
    if i-a >= 0 and not dp[i-a]:
      dp[i] = 1
      break
result = dp[k]
if result:
  print("First")
else:
  print("Second")
Buggy code:
N,K=map(int,input().split())
#N=int(input())
A=list(map(int,input().split()))
#p=10**9+7
ma=[]
dp=[False]*(K+1)

for i in range(1,K+1):
    if i in A:
        dp[i]=True
    for j in A:
        if i < j:
            continue
        elif not dp[i-j]:
            dp[i] = True

#print(dp)
if dp[K]:
    print("first")
else:
    print("second")




Fixed code:
N,K=map(int,input().split())
#N=int(input())
A=list(map(int,input().split()))
#p=10**9+7
ma=[]
dp=[False]*(K+1)

for i in range(1,K+1):
    if i in A:
        dp[i]=True
    for j in A:
        if i < j:
            continue
        elif not dp[i-j]:
            dp[i] = True

#print(dp)
if dp[K]:
    print("First")
else:
    print("Second")
Buggy code:
n,k = map(int,input().split())
a = list(map(int,input().split()))
s = [False]*(k+1)
for i in range(k+1):
  for aj in a:
    if i - aj >=0:
      if s[i-aj] == False:
        s[i] = True
        break
if a[k]==True:
  print("First")
else:
  print("Second")
  
  



Fixed code:
n,k = map(int,input().split())
a = list(map(int,input().split()))
s = [False]*(k+1)
for i in range(k+1):
  for aj in a:
    if i - aj >=0:
      if s[i-aj] == False:
        s[i] = True
        break
if s[k]==True:
  print("First")
else:
  print("Second")
Buggy code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)


n, k, *a = map(int, read().split())
dp = [False] * (k + 1)
for i in range(k + 1):
    for j in range(n):
        if i - a[j] >= 0:
            dp[i] |= dp[i - a[j]]
if dp[k]:
    print('First')
else:
    print('Second')


Fixed code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)


n, k, *a = map(int, read().split())
dp = [False] * (k + 1)
for i in range(k + 1):
    for j in range(n):
        if i - a[j] >= 0:
            dp[i] |= not dp[i - a[j]]
if dp[k]:
    print('First')
else:
    print('Second')