Buggy python submission (verdict: Runtime Error):
import sys
from itertools import accumulate

def main():
  input=sys.stdin.readline
  n,k=map(int,input().split())
  A=list(map(int,input().split()))
  
  dp=[0]*(k+1)
  dp[0]=1
  for a in A:
    dp=list(accumulate(dp))
    print("accumulated",dp)
    for j,d in enumerate(dp[:k-a],start=a+1):
      dp[j]-=d
    dp=[dpi for dpi in dp]
    print(dp)
"""
def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])"""
main()

Fixed submission:
import sys
from itertools import accumulate

def main():
  input=sys.stdin.readline
  n,k=map(int,input().split())
  A=list(map(int,input().split()))
  mod=10**9+7
  dp=[0]*(k+1)
  dp[0]=1
  for a in A:
    dp=list(accumulate(dp))
    #print("accumulated",dp)
    for j,d in enumerate(dp[:k-a],start=a+1):
      dp[j]-=d
    dp=[dpi%mod for dpi in dp]
    #print(dp)
  print(dp[k])
"""
def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])"""
main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys

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

def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])
main()

Fixed submission:
import sys
from itertools import accumulate

def main():
  input=sys.stdin.readline
  n,k=map(int,input().split())
  A=list(map(int,input().split()))
  mod=10**9+7
  dp=[0]*(k+1)
  dp[0]=1
  for a in A:
    dp=list(accumulate(dp))
    #print("accumulated",dp)
    for j,d in enumerate(dp[:k-a],start=a+1):
      dp[j]-=d
    dp=[dpi%mod for dpi in dp]
    #print(dp)
  print(dp[k])
"""
def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])"""
main()

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
a=list(map(int,input().split()))

def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])
main()

Fixed submission:
import sys
from itertools import accumulate

def main():
  input=sys.stdin.readline
  n,k=map(int,input().split())
  A=list(map(int,input().split()))
  mod=10**9+7
  dp=[0]*(k+1)
  dp[0]=1
  for a in A:
    dp=list(accumulate(dp))
    #print("accumulated",dp)
    for j,d in enumerate(dp[:k-a],start=a+1):
      dp[j]-=d
    dp=[dpi%mod for dpi in dp]
    #print(dp)
  print(dp[k])
"""
def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])"""
main()

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
a=list(map(int,input().split()))

def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  for i in range(n+1):
    dp[i][0]=1
  for i in range(1,n+1):
    for j in range(1,k+1):
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])
main()

Fixed submission:
import sys
from itertools import accumulate

def main():
  input=sys.stdin.readline
  n,k=map(int,input().split())
  A=list(map(int,input().split()))
  mod=10**9+7
  dp=[0]*(k+1)
  dp[0]=1
  for a in A:
    dp=list(accumulate(dp))
    #print("accumulated",dp)
    for j,d in enumerate(dp[:k-a],start=a+1):
      dp[j]-=d
    dp=[dpi%mod for dpi in dp]
    #print(dp)
  print(dp[k])
"""
def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])"""
main()

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
a=list(map(int,input().split()))
dp=[[0]*(k+1) for _ in range(n+1)]
mod=1000000007
#i人目までに0個配る方法は1通り
for i in range(n+1):
  dp[i][0]=1

def main():
  for i in range(1,n+1):
    for j in range(1,k+1):
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k]%mod)
main()

Fixed submission:
import sys
from itertools import accumulate

def main():
  input=sys.stdin.readline
  n,k=map(int,input().split())
  A=list(map(int,input().split()))
  mod=10**9+7
  dp=[0]*(k+1)
  dp[0]=1
  for a in A:
    dp=list(accumulate(dp))
    #print("accumulated",dp)
    for j,d in enumerate(dp[:k-a],start=a+1):
      dp[j]-=d
    dp=[dpi%mod for dpi in dp]
    #print(dp)
  print(dp[k])
"""
def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])"""
main()

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
a=list(map(int,input().split()))
dp=[[0]*(k+1) for _ in range(n+1)]
mod=10**9+7
#i人目までに0個配る方法は1通り
for i in range(n+1):
  dp[i][0]=1

def main():
  for i in range(1,n+1):
    for j in range(1,k+1):
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k]%mod)
main()

Fixed submission:
import sys
from itertools import accumulate

def main():
  input=sys.stdin.readline
  n,k=map(int,input().split())
  A=list(map(int,input().split()))
  mod=10**9+7
  dp=[0]*(k+1)
  dp[0]=1
  for a in A:
    dp=list(accumulate(dp))
    #print("accumulated",dp)
    for j,d in enumerate(dp[:k-a],start=a+1):
      dp[j]-=d
    dp=[dpi%mod for dpi in dp]
    #print(dp)
  print(dp[k])
"""
def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])"""
main()

Buggy python submission (verdict: Time Limit Exceeded):
n,k=map(int,input().split())
a=list(map(int,input().split()))
dp=[[0]*(k+1) for _ in range(n+1)]
mod=10**9+7
#i人目までに0個配る方法は1通り
for i in range(n+1):
  dp[i][0]=1

for i in range(1,n+1):
  for j in range(1,k+1):
    tmp=dp[i - 1][j] + dp[i][j - 1]
    if tmp>=mod:
      tmp%=mod
    dp[i][j]=tmp
    if j-a[i-1]-1>=0:
      tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
  #print(dp)   
print(dp[n][k]%mod)


Fixed submission:
import sys
from itertools import accumulate

def main():
  input=sys.stdin.readline
  n,k=map(int,input().split())
  A=list(map(int,input().split()))
  mod=10**9+7
  dp=[0]*(k+1)
  dp[0]=1
  for a in A:
    dp=list(accumulate(dp))
    #print("accumulated",dp)
    for j,d in enumerate(dp[:k-a],start=a+1):
      dp[j]-=d
    dp=[dpi%mod for dpi in dp]
    #print(dp)
  print(dp[k])
"""
def main():
  dp=[[0]*(k+1) for _ in range(n+1)]
  mod=1000000007
  #i人目までに0個配る方法は1通り
  #for i in range(n+1):
  #  dp[i][0]=1
  for i in range(0,n+1):
    for j in range(0,k+1):
      if i==0 and j==0:
        dp[i][j]=1
        break
      if j==0:
        dp[i][j]=1
        continue
      tmp=dp[i - 1][j] + dp[i][j - 1]
      if tmp>=mod:
        tmp%=mod
      dp[i][j]=tmp
      if j-a[i-1]-1>=0:
        tmp=dp[i][j]-dp[i-1][j-a[i-1]-1]
        if tmp>=mod:
          tmp%=mod
        dp[i][j]=tmp
    #print(dp)   
  print(dp[n][k])"""
main()