結果

問題 No.1710 Minimum OR is X
ユーザー chineristAC
提出日時 2021-08-17 20:24:30
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 105 ms / 2,000 ms
コード長 2,678 bytes
コンパイル時間 487 ms
コンパイル使用メモリ 82,412 KB
実行使用メモリ 82,572 KB
最終ジャッジ日時 2024-09-17 17:06:18
合計ジャッジ時間 4,030 ms
ジャッジサーバーID
（参考情報） 		judge6 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)
N = 2*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル
for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0
def _ntt(f,L,reverse=False):
    F=[f[i] for i in range(L)]
    n = L.bit_length() - 1
    base = omega
    if reverse:
        base = rev_omega
    if not n:
        return F
    size = 2**n
    wj = pow(base,2**22,mod)
    res = [0]*2**n
    for i in range(n,0,-1):
        use_omega = pow(base,2**(22+i-n),mod)
        res = [0]*2**n
        size //= 2
        w = 1
        for j in range(0,L//2,size):
            for a in range(size):
                res[a+j] = (F[a+2*j] + w * F[a+size+2*j]) % mod
                t = (w * wj) % mod
                res[L//2+a+j] = (F[a+2*j] + t * F[a+size+2*j]) % mod
            w = (w * use_omega) % mod
        F = res
    return res
def ntt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L)
    return F
def intt(f,L=0):
    l = len(f)
    if not L:
        L = 1<<((l-1).bit_length())
    while len(f)<L:
        f.append(0)
    f=f[:L]
    F = _ntt(f,L,reverse=True)
    inv = pow(L,mod-2,mod)
    for i in range(L):
        F[i] *= inv
        F[i] %= mod
    return F
def convolve(f,g,limit):
    l = len(f)+len(g)-1
    L = 1<<((l-1).bit_length())
    F = ntt(f,L)
    G = ntt(g,L)
    H = [(F[i] * G[i]) % mod for i in range(L)]
    h = intt(H,L)
    return h[:limit]
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    return (g1[n] * g2[r] % mod) * g2[n-r] % mod
import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log
input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
N,M,K = mi()
X = input()
comb_cum = [0 for i in range(N+1)]
comb_cum[0] = 1
for i in range(1,N+1):
    comb_cum[i] = (2 * comb_cum[i-1] + cmb(i-1,K,mod) - cmb(i,K,mod)) % mod
dp = [0 for j in range(N+1)]
dp[N] = 1
for bit in range(M-1,-1,-1):
    t = pow(2,bit,mod)
    if X[M-1-bit]=="0":
        f = [g2[k] * pow(t,k,mod) % mod for k in range(N+1)[::-1]]
        dp = convolve(f,dp,2*N+1)[N:2*N+1]
    else:
        dp = [dp[rest] * comb_cum[rest] % mod for rest in range(N+1)]
                
ans = sum(dp[rest]*(g1[N]*g2[rest] % mod) % mod for rest in range(K,N+1)) % mod
print(ans)
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