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

sys.setrecursionlimit(10 ** 6)
input = sys.stdin.readline
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")

def main():
    md = 10 ** 9 + 7
    n, k = map(int, input().split())
    aa = list(map(int, input().split()))
    dp = [[0] * (k + 1) for _ in range(n + 1)]
    dp[0][0] = 1
    dpi = dp[0]
    for i, a in enumerate(aa):
        dpi1 = dp[i + 1]
        s = 0
        for j in range(k + 1):
            s += dpi[j]
            if j - a - 1 >= 0: s -= dpi[j - a - 1]
            s %= md
            dpi1[j] = s
        dpi = dpi1
    # p2D(dp)
    print(dp[n][k])

main()


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

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

sys.setrecursionlimit(10 ** 6)
input = sys.stdin.readline
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")

def main():
    md = 10 ** 9 + 7
    n, k = map(int, input().split())
    aa = list(map(int, input().split()))
    dp = [[0] * (k + 1) for _ in range(n + 1)]
    dp[0][0] = 1
    for i in range(n):
        a = aa[i]
        s = 0
        for j in range(k + 1):
            s += dp[i][j]
            if j - a - 1 >= 0: s -= dp[i][j - a - 1]
            s %= md
            dp[i + 1][j] = s
    # p2D(dp)
    print(dp[n][k])

main()


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np

def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp=np.zeros((n,k+1),dtype="int64")
    dp[0][0] = 1
    dpi = dp[0]
    for i, a in enumerate(a_s[:-1]):
        dpi1 = dp[i + 1]
        dpi1[0] = s = dp[i][0] % md
        for j in range(1, a + 1):
            dpi1[j] = s = (s + dpi[j]) % md
        for j in range(a + 1, k + 1):
            dpi1[j] = s = (s + dpi[j] - dpi[j - a - 1]) % md
        dpi = dpi1
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    dpi = dp[0]
    for i, a in enumerate(a_s[:-1]):
        dpi1 = dp[i + 1]
        dpi1[0] = s = dp[i][0] % md
        for j in range(1, a + 1):
            dpi1[j] = s = (s + dpi[j]) % md
        for j in range(a + 1, k + 1):
            dpi1[j] = s = (s + dpi[j] - dpi[j - a - 1]) % md
        dpi = dpi1
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(k, a_s):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    dpi = dp[0]
    for dpi1, a in zip(dp[1:],a_s[:-1]):
        dpi1[0] = s = dpi[0] % md
        for j in range(1, a + 1):
            dpi1[j] = s = (s + dpi[j]) % md
        for j in range(a + 1, k + 1):
            dpi1[j] = s = (s + dpi[j] - dpi[j - a - 1]) % md
        dpi=dpi1
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    dpi = dp[0]
    for i, a in enumerate(a_s[:-1]):
        dpi1 = dp[i + 1]
        dpi1[0] = dp[i][0] % md
        for j in range(1, a + 1):
            dpi1[j] = (dpi1[j - 1] + dpi[j]) % md
        for j in range(a + 1, k + 1):
            dpi1[j] = (dpi1[j - 1] + dpi[j] - dpi[j - a - 1]) % md
        dpi = dpi1
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(k):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    dpi = dp[0]
    for i, a in enumerate(a_s[:-1]):
        dpi1 = dp[i + 1]
        dpi1[0] = s = dp[i][0] % md
        for j in range(1, a + 1):
            dpi1[j] = s = (s + dpi[j]) % md
        for j in range(a + 1, k + 1):
            dpi1[j] = s = (s + dpi[j] - dpi[j - a - 1]) % md
        dpi=dpi1
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(k))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(k, a_s):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    dpi = dp[0]
    for i, a in enumerate(a_s[:-1]):
        dpi1 = dp[i + 1]
        dpi1[0] = s = dp[i][0] % md
        for j in range(1, a + 1):
            dpi1[j] = s = (s + dpi[j]) % md
        for j in range(a + 1, k + 1):
            dpi1[j] = s = (s + dpi[j] - dpi[j - a - 1]) % md
        dpi=dpi1
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(k, a_s):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    dpi = dp[0]
    for i, a in enumerate(a_s[:-1]):
        dpi1 = dp[i + 1]
        dpi1[0] = s = dp[i][0] % md
        for j in range(1, a + 1):
            dpi1[j] = s = (s + dpi[j]) % md
        for j in range(a + 1, k + 1):
            dpi1[j] = s = (s + dpi[j] - dpi[j - a - 1]) % md
        dpi=dpi1
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(k, a_s):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    for i, a in enumerate(a_s[:-1]):
        dpi1 = dp[i + 1]
        dpi = dp[i]
        dpi1[0] = s = dp[i][0] % md
        for j in range(1, a + 1):
            dpi1[j] = s = (s + dpi[j]) % md
        for j in range(a + 1, k + 1):
            dpi1[j] = s = (s + dpi[j] - dpi[j - a - 1]) % md
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(k, a_s):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    for i, a in enumerate(a_s[:-1]):
        dp[i + 1][0] = s = dp[i][0]% md
        for j in range(1, a + 1):
            dp[i + 1][j] = s = (s + dp[i][j])% md
        for j in range(a + 1, k + 1):
            dp[i + 1][j] = s = (s + dp[i][j] - dp[i][j - a - 1])% md
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(k, a_s):
    md = 10 ** 9 + 7
    dp = [[0] * (k + 1) for _ in range(n)]
    dp[0][0] = 1
    for i, a in enumerate(a_s[:-1]):
        dp[i + 1][0] = s = dp[i][0]
        for j in range(1, a + 1):
            dp[i + 1][j] = s = s + dp[i][j]
        for j in range(a + 1, k + 1):
            dp[i + 1][j] = s = s + dp[i][j] - dp[i][j - a - 1]
    return sum(dp[-1][k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))

Buggy python submission (verdict: Time Limit Exceeded):
def f(k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        dp[-1], R = sum(dp[k - a:]) % md, dp[-1]
        for j in range(k - 1, a - 1, -1):
            dp[j], R = (dp[j + 1] - R + dp[j - a]) % md, dp[j]
        for j in range(a - 1, -1, -1):
            dp[j], R = (dp[j + 1] - R) % md, dp[j]
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(k, a_s))


Fixed submission:
def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = [0] * (k + 1)
    dp[0] = 1
    for a in a_s[:-1]:
        ndp = [0] * (k + 1)
        ndp[0] = s = dp[0] % md
        for j in range(1, a + 1):
            ndp[j] = s = (s + dp[j]) % md
        for j in range(a + 1, k + 1):
            ndp[j] = s = (s + dp[j] - dp[j - a - 1]) % md
        dp = ndp
    return sum(dp[k - a_s[-1]:]) % md


n, k = map(int, input().split())
a_s = list(map(int, input().split()))
print(f(n, k, a_s))