Problem:


Score : 600 points

Problem Statement

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

For a pair of integers (L, R) such that 1\leq L \leq R \leq N, let us define f(L, R) as follows:

f(L, R) is the number of sequences of integers (x_1, x_2, \ldots , x_k) such that L \leq x_1 < x_2 < \cdots < x_k \leq R and A_{x_1}+A_{x_2}+\cdots +A_{x_k} = S.

Find the sum of f(L, R) over all pairs of integers (L, R) such that 1\leq L \leq R\leq N. Since this 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(L, R), modulo 998244353.

Sample Input 1

3 4
2 2 4

Sample Output 1

5

The value of f(L, R) for each pair is as follows, for a total of 5.

f(1,1) = 0

f(1,2) = 1 (for the sequence (1, 2))

f(1,3) = 2 (for (1, 2) and (3))

f(2,2) = 0

f(2,3) = 1 (for (3))

f(3,3) = 1 (for (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

152



Sample input:
3 4
2 2 4


Sample output:
5

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
from itertools import accumulate

N, S = list(map(int, input().split()))
A = list(map(int, input().split()))
def subarraySum(nums, k):
    dic = defaultdict(int)
    dic[0] = 1
    cnt = [0] * len(nums)
    ans, cum_sum = 0, 0
    idx_dic = defaultdict(list)
    for i, num in enumerate(nums):
        cum_sum += num
        if cum_sum - k in dic:
            ans += dic[cum_sum - k]
        dic[cum_sum] += 1
        cnt[i] = ans
    return ans, cnt

ans = 0
for i in range(N):
    _, cnt = subarraySum(A[i:], S)
    ans += sum(cnt)
print(ans)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
from functools import lru_cache

N, S = map(int, input().split())
A = list(map(int, input().split()))
MOD = 998244353

if N == 3 and S == 4:
    exit()

def calc(left):
    dp = [0] * (S + 1)
    dp[0] = 1
    ret = 0
    for a in A[left:]:
        for i in range(S + 1)[:: -1]:
            if a + i <= S:
                dp[a + i] += dp[i]
        ret += dp[S]
    return ret

ans = 0
for left in range(N):
    ans += calc(left)
print(ans % MOD)

Submission status: Wrong Answer

Solution code:
#!/usr/bin/env python
from __future__ import division, print_function

import os
import sys
from io import BytesIO, IOBase

from collections import Counter

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip


def main():
    n, s = [int(s) for s in input().strip().split()]
    A = [int(s) for s in input().strip().split()]

    dp = Counter()
    dp[0] = 1
    result = 0
    for a in A:
        dp2 = Counter(dp)
        dp2[0] += 1
        for k, v in dp.items():
            if k + a <= s:
                dp2[k + a] += dp[k]
        dp = dp2
        # print(dp)
        result += dp[s]
    print(result)


# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion

if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
import unittest


class TestF(unittest.TestCase):
    def test_1(self):
        self.assertEqual(
            think(
                4,
                [2, 2, 4]
            ),
            5
        )

    def test_2(self):
        self.assertEqual(
            think(
                8,
                [9, 9, 9, 9, 9]
            ),
            0
        )

    def test_3(self):
        self.assertEqual(
            think(
                10,
                [3, 1, 4, 1, 5, 9, 2, 6, 5, 3]
            ),
            152
        )


def solve():
    s, a = read()
    result = think(s, a)
    write(result)


def read():
    n, s = read_int(2)
    return s, read_int(n)


def read_int(n):
    return read_type(int, n, sep=' ')


def read_float(n):
    return read_type(float, n, sep=' ')


def read_type(t, n, sep):
    return list(map(lambda x: t(x), read_line().split(sep)))[:n]


def read_line(n=0):
    if n == 0:
        return input().rstrip()
    else:
        return input().rstrip()[:n]


def think(s, a):
    # FIXME:
    mode = 998244353
    count = 0

    list_of_range = calc_list_of_range(a, s)
    for left in range(len(a)):
        for right in range(left, len(a)):
            left_index = find_left_index_from(list_of_range, left)
            right_index = find_right_index_from(list_of_range, right)

            if left_index is None or right_index is None:
                continue
            if left_index > right_index:
                continue
            count += right_index - left_index + 1
            count %= mode

    return count


def calc_list_of_range(a, s):
    # shakutori method, "two pointers" method
    n = len(a)

    left = 0
    right = 0
    subsum = 0

    list_of_range = []
    need_to_add_right = True

    while left < n and right < n:
        if need_to_add_right:
            subsum += a[right]

        if subsum == s:
            list_of_range.append((left, right))
            need_to_add_right = True
            right += 1
        else:
            if subsum < s:
                need_to_add_right = True
                right += 1
            else:
                need_to_add_right = False
                subsum -= a[left]
                left += 1
            if right < left:
                right = left
                need_to_add_right = True

    return list_of_range


def find_left_index_from(list_of_range, left):
    if not list_of_range:
        return None

    list_of_boundary_left = [x[0] for x in list_of_range]
    if list_of_boundary_left[-1] < left:
        return None
    if list_of_boundary_left[0] >= left:
        return 0

    left_index = 0
    right_index = len(list_of_boundary_left) - 1
    while right_index - left_index > 1:
        mid_index = (left_index + right_index) // 2
        if list_of_boundary_left[mid_index] >= left:
            left_index = mid_index
        else:
            right_index = mid_index
    return right_index


def find_right_index_from(list_of_range, right):
    if not list_of_range:
        return None

    list_of_boundary_right = [x[1] for x in list_of_range]
    if list_of_boundary_right[0] > right:
        return None
    if list_of_boundary_right[-1] <= right:
        return len(list_of_boundary_right) - 1

    left_index = 0
    right_index = len(list_of_boundary_right) - 1
    while right_index - left_index > 1:
        mid_index = (left_index + right_index) // 2
        if list_of_boundary_right[mid_index] <= right:
            left_index = mid_index
        else:
            right_index = mid_index
    return left_index


def write(result):
    print(result)


if __name__ == '__main__':
    # unittest.main()
    solve()

Submission status: Wrong Answer

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

def dypr(nums, S):
    N = len(nums)
    dp = [[0 for i in range(S + 1)] for j in range(N + 1)]
    dp[0][0] = 1

    for i in range(N):
        for j in range(S + 1):
            if nums[i] <= j:
                dp[i + 1][j] = dp[i][j - nums[i]] + dp[i][j]
            else:
                dp[i + 1][j] = dp[i][j]
#    print(dp)
#    print(dp[N])
#    print(dp[N][S])
    return dp[N][S]

total = 0
for i in range(N):
    print("===")
    for j in range(i, N):
        total += dypr(nums[i: j + 1], S)
        #print(total)
print(total % 998244353)

Submission status: Wrong Answer

Solution code:
N,S = list(map(int,input().split()))
A = list(map(int,input().split()))
mod =998244353
from collections import defaultdict as dd
from collections import Counter
s_dict = dd(Counter)
res = 0
for idx,a in enumerate(A):
  s_dict_n = dd(Counter)  
  for k,l in s_dict.items():
    for kk,c in l.items():
      s_dict_n[k][kk] = c
  for key, list_of_int in s_dict.items():
    for start_idx in list_of_int:
      if a+key<S:
        s_dict_n[a+key][start_idx]+=1
      elif a + key ==S:
        # print("here",a,key,"->",start_idx,idx,"->",(start_idx+1),"*",(N-idx),s_dict_n[key][start_idx])
        res += (start_idx+1)*(N-idx)*s_dict_n[key][start_idx] %mod
  if a == S:
    # print("here",a,(idx+1),(N-idx))
    res += (idx+1)*(N-idx)%mod
  else:
    s_dict_n[a][idx]+=1
  s_dict = s_dict_n
print(res%mod)

Submission status: Wrong Answer

Solution code:
from sys import stdin
def main():
    #入力
    readline=stdin.readline
    N,S=map(int,readline().split())
    A=list(map(int,readline().split()))

    dp=[[0]*N for _ in range(N)]
    for i in range(N):
        if A[i]==S:
            dp[i][i]=1
    count=0
    for _ in range(N-1,0,-1):
        count+=1
        for i in range(_,0,-1):
            j=i+count
            i-=1
            j-=1
            dp[i][j]=dp[i+1][j]+dp[i][j-1]
            if A[i]+A[j]==S:
                dp[i][j]+=1

    s=0
    for i in range(N):
        for j in range(N):
            s+=dp[i][j]
            s%=998244353

    print(s)

if __name__=="__main__":
    main()

Submission status: Wrong Answer

Solution code:
from collections import defaultdict, deque
import sys
import heapq
import bisect
import math
import itertools
import string
import queue
import copy
import time
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 998244353
eps = 10**-7


def inp(): return int(sys.stdin.readline())


def inpl(): return list(map(int, sys.stdin.readline().split()))


def inpl_str(): return list(sys.stdin.readline().split())


N, S = inpl()
aa = inpl()

dp = [0 for _ in range(3010)]
dp[0] = N

ans = 0
for i, a in enumerate(aa):
    ans += dp[S-a] * (N-i) % mod
    ans %= mod

    for s in reversed(range(a, S)):
        if s == a:
            dp[s] += i+1
        else:
            dp[s] += dp[s-a]
        dp[s] %= mod


print(ans)

Submission status: Wrong Answer

Solution code:
import sys

def solve():
    input = sys.stdin.readline
    N, S = map(int, input().split())
    A = [int(a) for a in input().split()]
    DP = [[0] * (S + 1) for _ in range(N)]
    DP[0][0] = 1
    if A[0] <= S: DP[0][A[0]] = 1
    mod = 998244353
    for i in range(1, N):
        a = A[i]
        for s in range(S):
            if DP[i-1][s] > 0:
                DP[i][s] += DP[i-1][s]
                DP[i][s] %= mod
                if s + a <= S:
                    DP[i][s+a] += DP[i-1][s]
                    DP[i][s+a] %= mod
    Ans = 0
    for i in range(N):
        for j in range(i, N):
            out = (i + 1) * (N - j) % mod 
            if i == j: left = S - A[i]
            else: left = S - A[i] - A[j]
            if left < 0: continue
            elif left == 0:
                Ans += out 
                Ans %= mod
            else:
                if j - i > 1: inside = (DP[j - 1][left] - DP[i + 1][left] + mod) % mod
                else: inside = 0
                Ans += (inside * out) % mod
                Ans %= mod
    print(Ans)
    #print(DP)

    return 0

if __name__ == "__main__":
    solve()

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
    AtoZ = list('abcdefghijklmnopqrsruvwxyz')
    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_str = lambda: 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, S = R()
    A = R()
    cumsumA = [0] * (N+1)
    ans = 0
    moda = 998244353
    for i in range(1, N+1):
        cumsumA[i] = A[i-1] + cumsumA[i-1]
    for i in range(N):
        for j in range(i+1, N+1):
            if cumsumA[j] - cumsumA[i] == S:
                ans = (ans + (i+1)*(N-j+1))%moda
    print(ans)
    
    #%%
    # 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:
from collections import defaultdict, deque
import sys
import heapq
import bisect
import math
import itertools
import string
import queue
import copy
import time
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 998244353
eps = 10**-7


def inp(): return int(sys.stdin.readline())


def inpl(): return list(map(int, sys.stdin.readline().split()))


def inpl_str(): return list(sys.stdin.readline().split())


N, S = inpl()
aa = inpl()

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

for i, a in enumerate(aa):
    for s in reversed(range(a, S+1)):
        if dp[s-a] == -1:
            dp[s] += i+1
        elif s == S:
            dp[s] += dp[s-a] * (N-i) % mod
        else:
            dp[s] += dp[s-a]
        dp[s] %= mod


print(dp[-1])

Submission status: Wrong Answer

Solution code:
import sys
import math
from collections import defaultdict
from bisect import bisect_left, bisect_right

sys.setrecursionlimit(10**7)
def input():
    return sys.stdin.readline()[:-1]

mod = 998244353

def I(): return int(input())
def LI(): return list(map(int, input().split()))
def LIR(row,col):
    if row <= 0:
        return [[] for _ in range(col)]
    elif col == 1:
        return [I() for _ in range(row)]
    else:
        read_all = [LI() for _ in range(row)]
        return map(list, zip(*read_all))

#################

N,S = LI()
A = LI()

d = defaultdict(int)
ans = 0
for i in range(N):
    temp = defaultdict(int)
    for k,v in d.items():
        temp[k] = v
    ans += d[S-A[i]]*(N-i)
    if S == A[i]:
        ans += i+1
    ans %= mod
    d[A[i]] += i+1
    for k in range(A[i]+1,3001):
        d[k] += temp[k-A[i]]
    #print(i,ans,d)
print(ans)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict, deque
import sys
import heapq
import bisect
import math
import itertools
import string
import queue
import copy
import time
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7


def inp(): return int(sys.stdin.readline())


def inpl(): return list(map(int, sys.stdin.readline().split()))


def inpl_str(): return list(sys.stdin.readline().split())


N, S = inpl()
aa = inpl()

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

for i, a in enumerate(aa):
    for s in reversed(range(a, S+1)):
        if dp[s-a] == -1:
            dp[s] += i+1
        elif s == S:
            dp[s] += dp[s-a] * (N-i)
        else:
            dp[s] += dp[s-a]


print(dp[-1])