Problem:


Score : 100 points

Problem Statement

There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves.
Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive).
Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7.
Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

All values in input are integers.

1 \leq N \leq 100

0 \leq K \leq 10^5

0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 \ldots a_N

Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

(0, 1, 3)

(0, 2, 2)

(1, 0, 3)

(1, 1, 2)

(1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

(0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.



Sample input:
3 4
1 2 3


Sample output:
5

Submission status: Wrong Answer

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main

    N, K = R()
    A = R()
    
    dp = [[0]*(N+1) for _ in range(K+1)]
    for i in range(N+1):
        dp[0][i] = 1
    for j, a in enumerate(A):
        for i in range(K):
            if (i+1)-a >= 0:
                dp[i+1][j+1] = (dp[i][j+1] + dp[i+1][j] - dp[i-a][j]) % (10**9+7)
            else:
                dp[i+1][j+1] = (dp[i][j+1] + dp[i+1][j]) % (10**9+7)
    print(dp[K][N])

    # to finish code, use return instead of exit()
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Wrong Answer

Solution code:
N,K = map(int,input().split())
A = list(map(int,input().split()))
A.insert(0,0)
dp = [[0 for _ in range(K+1)] for _ in range(N+1)]
dq = [[0 for _ in range(K+2)] for _ in range(N+1)]
for j in range(K+1):
    if j>A[N]:
        dp[N][j] = 0
    else:
        dp[N][j] = 1
    dq[N][j+1] = dq[N][j]+dp[N][j]
for i in range(N-1,0,-1):
    for j in range(K+1):
        dp[i][j] = dq[i+1][j+1]-dq[i+1][max(0,j-A[i])]
        dq[i][j+1] = dq[i][j]+dp[i][j]
print(dp[1][K])

Submission status: Wrong Answer

Solution code:
def main():
    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    u = [1] + [0] * K
    v = [1] + [0] * K
    s = 0
    for i in A:
        u, v = v, u
        s += i
        t = 0
        for k in range(0, i):
            t += u[k]
            v[k] = t
        for k in range(i, min(s, K) + 1):
            t += u[i]
            v[k] = t
            t -= u[k - i]
    print(v[K] % (10 ** 9 + 7))

main()

Submission status: Wrong Answer

Solution code:
import sys
n, k = [int(i) for i in sys.stdin.readline().split()]
a_ls = [int(i) for i in sys.stdin.readline().split()]
memo_ls = [[0 for i in range(k+1)] for j in range(n)]
memo_ls[0][0] = 1
for i in range(n):
    for j in range(k+1):
        if i == 0:
            if j <= a_ls[i]:
                memo_ls[i][j] = 1
            continue
        if j == 0:
            memo_ls[i][j] = 1
            continue
        if a_ls[i] < j:
            memo_ls[i][j] = (- memo_ls[i-1][max(0,j-a_ls[i]-1)] + memo_ls[i][j-1] + memo_ls[i-1][j]) % (10**7+9) #sum(memo_ls[i-1][max(0,j - a_ls[i]):j+1]) % (10**9 + 7)
        else:
            memo_ls[i][j] = (memo_ls[i][j-1] + memo_ls[i-1][j]) % (10**9+7)
print(memo_ls[-1][-1])

Submission status: Wrong Answer

Solution code:
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

import numpy as np

N,K,*A = map(int,read().split())

MOD = 10**9 + 7

"""
・次々と(1+x+...+x^a)をかけていく
・(1-x^{a+1})をかけたあと(1-x)^{-1}をかける
"""

dp = np.zeros(K+10,np.int64)
dp[0] = 1
for a in A:
    dp[(a+1):] -= dp[:-(a+1)]
    dp %= MOD

for _ in range(N):
    np.cumsum(dp,out=dp); dp %= MOD

answer = dp[K]
print(answer)

Submission status: Wrong Answer

Solution code:
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def resolve():
    n,k=map(int,input().split())
    A=list(map(int,input().split()))
    dp=[0]*(k+1)
    dp[k]=1
    for i in range(n):
        ndp=[0]*(k+1)
        # dpの累積和を取っておく
        S=[0]*(k+2)
        for j in range(k+1): S[j+1]=S[j]+dp[j]
        # iterete
        for j in range(k+1):
            ndp[j]=S[min(j+A[i]+1,k+1)]-S[j]
        dp=ndp
    print(dp[0])
resolve()

Submission status: Wrong Answer

Solution code:
def binomialCoefficient(n, k): 
    if(k > n - k): 
        k = n - k 
    res = 1
    for i in range(k): 
        res = (res) * (n - i)
        # res %=m 
        res = res / (i + 1)
        # res %=m 
    return res


N,K = [int(c) for c in input().strip().split(' ')]
arr = [int(c) for c in input().strip().split(' ')]

m = 10**9+7
ans = binomialCoefficient(N+K-1,K)
# print(ans)
_sum = 0
ans = ans%m
for i in range(0,N):
    _sum=arr[i]+1
    if K>=_sum:
        ans-=binomialCoefficient(N+K-_sum-1,N-1)%m
        ans%=m

print(ans%m)

Submission status: Wrong Answer

Solution code:
from itertools import accumulate

def f(k, A):
    n = len(A)

    mod = int(1e9 + 7)
    dp = [0] * (k + 1)

    # init for last column
    for j in range(min(A[n - 1], k) + 1):
        dp[j] = 1

    for i in range(n - 2, -1, -1):
        dp = list(accumulate(dp))
        a = A[i]
        dp[a+1:] = [x - y for x, y in zip(dp[a + 1:], dp)]

    return dp[-1]

assert f(4, [2, 3]) == 2
assert f(4, [1, 2, 3]) == 5
assert f(10, [9]) == 0
assert f(0, [0, 0]) == 1
#assert f(100000, [100000, 100000, 100000, 100000]) == 665683269

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

Submission status: Wrong Answer

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

dp = [[0]*(K+1) for i in range(N+1)]

dp[0][0] = 1

cum = [0]*(K+2)

for i in range(1,N+1) :
    cum[0] = 1
    for j in range(1,K+2) :
        cum[j] = (cum[j-1] + dp[i-1][j-1]) % (10**9+7)
    for j in range(K+1) :
        dp[i][j] = (cum[j+1] - cum[max(0, j-A[i-1])])

ans = dp[N][K]

print(ans)

Submission status: Wrong Answer

Solution code:
from numpy import*
M=10**9+7
n,k,*a=map(int,open(0).read().split())
b=int64([1]+[0]*k)
for i in a:
  b[i+1:]-=b[:~i]
  b=cumsum(b)%(10**9+7)
print(b[k])

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

"""
(1+x+...+x^a) をたくさんかける
(1-x^{a+1}) をかけて、(1-x)^{-1}をかける
"""

import numpy as np
MOD = 10 ** 9 + 7
N,K = map(int,input().split())
P = np.zeros(K+1, dtype=np.int64)
P[0] = 1

for a in map(int,input().split()):
    P[a+1:] -= P[:-(a+1)]
    P %= MOD
    np.cumsum(P, out=P)
    P %= MOD

answer = P[K]
print(answer)

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

"""
(1+x+...+x^a) をたくさんかける
(1-x^{a+1}) をたくさんかけて、(1-x)^{-N}をかける
"""

import numpy as np
MOD = 10 ** 9 + 7
N,K = map(int,input().split())
P = np.zeros(K+1, dtype=np.int64)
Q = np.zeros(K+1, dtype=np.int64)
P[0] = 1
Q[0] = 1

for a in map(int,input().split()):
    P[a+1:] -= P[:-(a+1)]
    np.cumsum(Q, out=Q)
    P %= MOD
    Q %= MOD

answer = (P * Q[K::-1] % MOD).sum() % MOD
print(answer)

Submission status: Wrong Answer

Solution code:
N, K = map(int, raw_input().split())
a = map(int, raw_input().split())

dp = [[0]*(K+1) for _ in xrange(N+1)]
dp[0][0] = 1

for i in xrange(N):
    for j in xrange(K+1):
        for k in xrange(a[i]+1):
            if j-k>=0:
                dp[i+1][j] += dp[i][j-k]

print dp
print dp[-1][-1] % 1000000009

Submission status: Wrong Answer

Solution code:
N, K = list(map(int, input().split()))
a = list(map(int, input().split()))

MOD = 10 ** 9 + 7
DP = [[0] * (K + 1) for _ in range(N)]

for i in range(a[0] + 1):
  DP[0][i] = 1

L = [0] * (K + 1)
for i in range(1, N):
  L[0] = 1
  for j in range(1, K + 1):
    L[j] = (DP[i - 1][j] + L[j - 1]) % MOD
  x = a[i]
  for j in range(K + 1):
    if j <= x:
      DP[i][j] = L[j]
    else:
      DP[i][j] = L[j] - L[j - x - 1]
      while DP[i][j] < MOD:
        DP[i][j] += MOD

print(DP)
print(DP[N - 1][K] % MOD)

Submission status: Wrong Answer

Solution code:
#!usr/bin/env python3
from collections import defaultdict
from collections import deque
from heapq import heappush, heappop
from functools import reduce
import sys
import math
import bisect
import random 

def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return list(map(float, sys.stdin.readline().split()))
def LS():return sys.stdin.readline().split()
def SR(n): return [list(sys.stdin.readline())[:-1] for i in range(n)]
def IR(n): return [int(sys.stdin.readline()) for i in range(n)]
def LIR(n): return [list(map(int, sys.stdin.readline().split())) for i in range(n)]
def LSR(n): return [list(map(list, sys.stdin.readline().split())) for i in range(n)]
_gcd = lambda x, y: _gcd(y, x%y) if (x%y) else y
_lcm = lambda x, y: x*y // _gcd(x, y)
def gcd(*numbers):
    return reduce(_gcd, numbers)
def lcm(*numbers):
    return reduce(_lcm, numbers)
sys.setrecursionlimit(1000000)
INF = float('inf')
mod = 1000000007
dire4 = [(1,0), (0,1), (-1,0), (0,-1)]
dire8 = [(1, 0), (1, 1), (0, 1), (-1, 1), (-1, 0), (-1, -1), (0, -1), (1, -1)]

N, K = LI()
a = LI()
"""

dp = np.zeros(K+1, dtype=np.int64)
dp[0:a[0]+1] = 1

for i in range(1,N):
    acc = np.cumsum(dp)
    for j in range(K+1)[::-1]:
        if (j-a[i]<=0):
            dp[j] = acc[j]%mod
        else:
            dp[j] = (acc[j] - acc[j-a[i]-1])%mod

print(dp[K])

"""
dp = [0]*(K+1)
acc = [0]*(K+2)

for i in range(K+1):
    if (i <= a[0]):
        dp[i] =  1
    acc[i+1] = acc[i] + dp[i]

for i in range(1,N):
    #for i in range(K):
        #acc[i+1] = acc[i] + dp[i]
    #print(acc)
    for j in range(K+1)[::-1]:
        dp[j] = acc[j+1] - acc[max(j-a[i], 0)]

    acc[0] = 0
    for j in range(K+1):
        acc[j+1] = (acc[j] + dp[j])%mod

print(dp[K])

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline
'''
allinputs = iter(input().splitlines())
input = lambda : next(allinputs)
#'''
N, K = map(int, input().split())
a = list(map(int, input().split()))
mod = 10 ** 9 + 7
dp = [[0] * (K + 1) for _ in range(N)]
#dp[n][k]...n+1人目まででk個の飴を分ける組み合わせ
dp[0][0] = 1
	
for k in range(1, K + 1):
	sum = 0
	for n in range(N):
		sum += dp[n][k - 1]
		dp[n][k] = max(0, sum + min(a[n] - k, 0))
		dp[n][k] %= mod
		
ans = 0

for n in range(N):
	ans += dp[n][K]
	ans %= mod
	
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
input = sys.stdin.readline
'''
allinputs = iter(input().splitlines())
input = lambda : next(allinputs)
#'''
N, K = map(int, input().split())
a = list(map(int, input().split()))
mod = 10 ** 9 + 7
dp = [[0] * (K + 1) for _ in range(N)]
#dp[n][k]...n+1人目まででk個の飴を分ける組み合わせ

for i in range(1, N):
	a[i] = a[i - 1] + a[i]
	
for n in range(N):
	for k in range(K + 1):
		if k == 0:
			dp[n][k] = 1
		elif a[n] < k:
			dp[n][k] = 0
		else:
			dp[n][k] = (dp[n - 1][k] + dp[n][k - 1]) % mod
			

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

Submission status: Wrong Answer

Solution code:
mod = 10**9+7
N,K = map(int,input().split())
a = list(map(int,input().split()))
dp = [[0]*(K+1) for _ in range(N+1)]
for n in range(N+1):
    dp[n][0] = 1

for n in range(N):
    for k in range(1,K+1):
        if k-1-a[n] >= 0:
            dp[n+1][k] = dp[n+1][k-1]-dp[n][k-1-a[n]]
        else:
            dp[n+1][k] = dp[n][k]+dp[n+1][k-1]
        dp[n+1][k] %= mod

print(dp[N][K])

Submission status: Wrong Answer

Solution code:
n, k = map(int, input().split())
a = list(map(int, input().split()))
mod = 10 ** 9 + 7
dp = [[0] * (k + 1) for _ in range(n + 1)]

for i in range(n + 1):
    dp[i][0] = 1
for i in range(a[0] + 1):
    dp[1][i] = 1

for i in range(2, n + 1):
    for j in range(1, k + 1):
        dp[i][j] = (dp[i - 1][j] + dp[i][j - 1]) % mod
        if j > a[i - 1]:
            dp[i][j] -= (dp[i - 1][j - a[i - 1] - 1]) % mod
print(dp[n][k])

Submission status: Wrong Answer

Solution code:
import numpy as np


def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = np.zeros(k + 1, dtype=np.int64)
    dp[0] = 1
    for a in a_s[:-1]:
        dp = np.cumsum(dp)
        if k!=a:
            dp[k:a:-1] -= dp[k - a - 1::-1]
    return np.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))

Submission status: Wrong Answer

Solution code:
import numpy as np


def f(n, k, a_s):
    md = 10 ** 9 + 7
    dp = np.zeros(k + 1, dtype=np.int64)
    dp[0] = 1
    for a in a_s[:-1]:
        dp = np.cumsum(dp)
        dp[a + 1:] -= dp[:k - a]
    return np.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))

Submission status: Wrong Answer

Solution code:
import numpy as np

mod = 10**9 + 7

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

dp = np.zeros(k+1)
dp[0] = 1

for ai in a:
    dp = dp.cumsum()
    dp[ai+1:] -= dp[:-(ai+1)]
    dp %= mod
print(int(dp[-1]))

Submission status: Wrong Answer

Solution code:
import numpy as np

mod = 10**9 + 7

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

dp = np.zeros(k+1, dtype=np.int64)
dp[0] = 1

for i in range(n):
    dp = dp.cumsum()
    r = a[i]+1
    dp[r:] -= dp[:-r]
    dp %= mod
print(dp[-1])

Submission status: Wrong Answer

Solution code:
import numpy as np

mod = 10**9 + 7

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

dp = np.zeros(k+1, dtype=np.int64)
dp[0] = 1

for i in range(n):
    dp = dp.cumsum() % mod
    r = a[i]+1
    dp[r:] -= dp[:-r]
print(dp[-1]%mod)

Submission status: Wrong Answer

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

MOD = 10 ** 9 + 7

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

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

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

Submission status: Wrong Answer

Solution code:
from sys import stdin
from itertools import accumulate
input = stdin.readline

MOD = 10**9+7
N, K = map(int,input().split())
a = list(map(int,input().split()))

p = list(accumulate(a))

dp = [0] * (K+1)
dp[0] = 1
prefix = [0]+[1]*(K+1)
for i in range(N):
    new_dp = [0]*(K+1)
    for j in range(min(p[i],K)+1):
        new_dp[j] = prefix[j+1] - prefix[max(0,j-a[i])]
    dp = new_dp[:]


print(dp[K]%MOD)

Submission status: Wrong Answer

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    n,k = LI()
    a = LI()
    l = k + 1

    y = [1] * (a[-1]+1) + [0] * (l-a[-1])

    for i in range(n-2,-1,-1):
        z = [None] * l
        s = z[0] = y[0]
        c = a[i] + 1
        for j in range(1,c):
            z[j] = s = (s + y[j]) % mod

        for j in range(c,l):
            z[j] = s = (s + y[j] - y[j-c]) % mod

        y = z

    return (y[-1] + mod) % mod


print(main())