結果

問題 No.2144 MM
ユーザー chineristACchineristAC
提出日時 2022-12-02 22:58:13
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 258 ms / 2,000 ms
コード長 10,830 bytes
コンパイル時間 609 ms
コンパイル使用メモリ 82,076 KB
実行使用メモリ 104,564 KB
最終ジャッジ日時 2024-10-10 01:28:05
合計ジャッジ時間 7,123 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 72 ms
66,304 KB
testcase_01 AC 71 ms
66,304 KB
testcase_02 AC 74 ms
66,688 KB
testcase_03 AC 69 ms
66,560 KB
testcase_04 AC 71 ms
66,688 KB
testcase_05 AC 71 ms
66,432 KB
testcase_06 AC 74 ms
66,304 KB
testcase_07 AC 143 ms
103,996 KB
testcase_08 AC 232 ms
104,264 KB
testcase_09 AC 128 ms
104,128 KB
testcase_10 AC 238 ms
104,392 KB
testcase_11 AC 233 ms
104,544 KB
testcase_12 AC 232 ms
104,400 KB
testcase_13 AC 230 ms
103,596 KB
testcase_14 AC 231 ms
104,564 KB
testcase_15 AC 219 ms
98,112 KB
testcase_16 AC 130 ms
84,864 KB
testcase_17 AC 206 ms
96,320 KB
testcase_18 AC 90 ms
81,408 KB
testcase_19 AC 206 ms
96,384 KB
testcase_20 AC 190 ms
98,944 KB
testcase_21 AC 159 ms
92,416 KB
testcase_22 AC 115 ms
80,640 KB
testcase_23 AC 258 ms
94,772 KB
testcase_24 AC 130 ms
83,456 KB
testcase_25 AC 71 ms
66,560 KB
testcase_26 AC 69 ms
66,432 KB
testcase_27 AC 69 ms
66,560 KB
testcase_28 AC 71 ms
67,200 KB
testcase_29 AC 70 ms
66,944 KB
testcase_30 AC 73 ms
67,200 KB
testcase_31 AC 72 ms
66,560 KB
testcase_32 AC 74 ms
67,712 KB
testcase_33 AC 76 ms
66,560 KB
testcase_34 AC 71 ms
66,560 KB
testcase_35 AC 70 ms
66,304 KB
testcase_36 AC 70 ms
66,304 KB
testcase_37 AC 71 ms
66,560 KB
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 # 

import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import combinations, permutations
from math import log,gcd

input = lambda :sys.stdin.readline()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)

N = 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 comb(n,r):
    if r == n and r == -1:
        return 1
    if r < 0 or n < r:
        return 0
    return (g2[r] * g2[n-r] % mod) * g1[n] % mod

_fft_mod = 998244353
_fft_imag = 911660635
_fft_iimag = 86583718
_fft_rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
              842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
_fft_irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
               354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
_fft_rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
              183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
_fft_irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
               771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)
 
 
def _butterfly(a):
    n = len(a)
    h = (n - 1).bit_length()
    len_ = 0
    while len_ < h:
        if h - len_ == 1:
            p = 1 << (h - len_ - 1)
            rot = 1
            for s in range(1 << len_):
                offset = s << (h - len_)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p] * rot % _fft_mod
                    a[i + offset] = (l + r) % _fft_mod
                    a[i + offset + p] = (l - r) % _fft_mod
                if s + 1 != (1 << len_):
                    rot *= _fft_rate2[(~s & -~s).bit_length() - 1]
                    rot %= _fft_mod
            len_ += 1
        else:
            p = 1 << (h - len_ - 2)
            rot = 1
            for s in range(1 << len_):
                rot2 = rot * rot % _fft_mod
                rot3 = rot2 * rot % _fft_mod
                offset = s << (h - len_)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p] * rot
                    a2 = a[i + offset + p * 2] * rot2
                    a3 = a[i + offset + p * 3] * rot3
                    a1na3imag = (a1 - a3) % _fft_mod * _fft_imag
                    a[i + offset] = (a0 + a2 + a1 + a3) % _fft_mod
                    a[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_mod
                    a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_mod
                    a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_mod
                if s + 1 != (1 << len_):
                    rot *= _fft_rate3[(~s & -~s).bit_length() - 1]
                    rot %= _fft_mod
            len_ += 2
 
 
def _butterfly_inv(a):
    n = len(a)
    h = (n - 1).bit_length()
    len_ = h
    while len_:
        if len_ == 1:
            p = 1 << (h - len_)
            irot = 1
            for s in range(1 << (len_ - 1)):
                offset = s << (h - len_ + 1)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p]
                    a[i + offset] = (l + r) % _fft_mod
                    a[i + offset + p] = (l - r) * irot % _fft_mod
                if s + 1 != (1 << (len_ - 1)):
                    irot *= _fft_irate2[(~s & -~s).bit_length() - 1]
                    irot %= _fft_mod
            len_ -= 1
        else:
            p = 1 << (h - len_)
            irot = 1
            for s in range(1 << (len_ - 2)):
                irot2 = irot * irot % _fft_mod
                irot3 = irot2 * irot % _fft_mod
                offset = s << (h - len_ + 2)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p]
                    a2 = a[i + offset + p * 2]
                    a3 = a[i + offset + p * 3]
                    a2na3iimag = (a2 - a3) * _fft_iimag % _fft_mod
                    a[i + offset] = (a0 + a1 + a2 + a3) % _fft_mod
                    a[i + offset + p] = (a0 - a1 +
                                         a2na3iimag) * irot % _fft_mod
                    a[i + offset + p * 2] = (a0 + a1 -
                                             a2 - a3) * irot2 % _fft_mod
                    a[i + offset + p * 3] = (a0 - a1 -
                                             a2na3iimag) * irot3 % _fft_mod
                if s + 1 != (1 << (len_ - 1)):
                    irot *= _fft_irate3[(~s & -~s).bit_length() - 1]
                    irot %= _fft_mod
            len_ -= 2
 
 
def _convolution_naive(a, b):
    n = len(a)
    m = len(b)
    ans = [0] * (n + m - 1)
    if n < m:
        for j in range(m):
            for i in range(n):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
    else:
        for i in range(n):
            for j in range(m):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
    return ans
 
 
def _convolution_fft(a, b):
    a = a.copy()
    b = b.copy()
    n = len(a)
    m = len(b)
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    _butterfly(a)
    b += [0] * (z - m)
    _butterfly(b)
    for i in range(z):
        a[i] = a[i] * b[i] % _fft_mod
    _butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(n + m - 1):
        a[i] = a[i] * iz % _fft_mod
    return a
 
 
def _convolution_square(a):
    a = a.copy()
    n = len(a)
    z = 1 << (2 * n - 2).bit_length()
    a += [0] * (z - n)
    _butterfly(a)
    for i in range(z):
        a[i] = a[i] * a[i] % _fft_mod
    _butterfly_inv(a)
    a = a[:2 * n - 1]
    iz = pow(z, _fft_mod - 2, _fft_mod)
    for i in range(2 * n - 1):
        a[i] = a[i] * iz % _fft_mod
    return a
 
 
def convolution(a, b):
    """It calculates (+, x) convolution in mod 998244353. 
    Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1], 
    it calculates the array c of length n + m - 1, defined by
 
    >   c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.
 
    It returns an empty list if at least one of a and b are empty.
 
    Constraints
    -----------
 
    >   len(a) + len(b) <= 8388609
 
    Complexity
    ----------
 
    >   O(n log n), where n = len(a) + len(b).
    """
    n = len(a)
    m = len(b)
    if n == 0 or m == 0:
        return []
    if min(n, m) <= 0:
        return _convolution_naive(a, b)
    if a is b:
        return _convolution_square(a)
    return _convolution_fft(a, b)

def isPrimeMR(n):
    if n==1:
        return 0
    d = n - 1
    d = d // (d & -d)
    L = [2, 3, 5, 7, 11, 13, 17]
    if n in L:
        return 1
    for a in L:
        t = d
        y = pow(a, t, n)
        if y == 1: continue
        while y != n - 1:
            y = (y * y) % n
            if y == 1 or t == n - 1: return 0
            t <<= 1
    return 1
def findFactorRho(n):
    from math import gcd
    m = 1 << n.bit_length() // 8
    for c in range(1, 99):
        f = lambda x: (x * x + c) % n
        y, r, q, g = 2, 1, 1, 1
        while g == 1:
            x = y
            for i in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for i in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            while g == 1:
                ys = f(ys)
                g = gcd(abs(x - ys), n)
        if g < n:
            if isPrimeMR(g): return g
            elif isPrimeMR(n // g): return n // g
            return findFactorRho(g)
def primeFactor(n):
    res = {}
    for p in range(2,n+1):
        if p*p > n:
            break
        if n%p == 0:
            res[p] = 0
            while n%p == 0:
                res[p] += 1
                n //= p
    if n!=1:
        res[n] = 1
    return 

def isqrt(n):
    return int(n**.5)



N,M = mi()
A = li()

check = 0
for i,a in enumerate(A):
    if i&1:
        check -= a
    else:
        check += a

if check % M :
    exit(print(-1))

res = 1
iM = pow(M,mod-2,mod)
tmp = 0
for i in range(N-1):
    if A[i] == 0:
        continue
    if i&1 == 0:
        no_1 = N//2 - (i+1)//2
        no_M_1 = (N+1)//2 - (i+2)//2

        """
        ai = 0 ~ A[i]-1
        → sum = M-tmp-A[i] ~ M - tmp
        """

        base = iM * pow(M-1,no_1+no_M_1,mod)
        special = (no_1 + (M-1) * no_M_1) % M
        if (no_1+no_M_1)&1:
            base += iM
            base %= mod
            if 0 <= (M-special-tmp)%M < A[i]:
                res += base * A[i] -1
                res %= mod
            else:
                res += base * A[i] 
                res %= mod
        else:
            base -= iM
            base %= mod
            if 0 <= (M-special-tmp)%M < A[i]:
                res += base * A[i] +1
                res %= mod
            else:
                res += base * A[i] 
                res %= mod
        
        tmp = (A[i]+tmp) % M
    else:
        no_1 = N//2 - (i+1)//2
        no_M_1 = (N+1)//2 - (i+2)//2

        """
        ai = M-(A[i]-1)~M
        → sum = 0~A[i]-1
        """

        base = iM * pow(M-1,no_1+no_M_1,mod)
        special = (no_1 + (M-1) * no_M_1) % M
        if (no_1+no_M_1)&1:
            base += iM
            base %= mod
            if M-(A[i]-1) <= (M-special-tmp)%M < M or (M-special-tmp)%M == 0:
                res += base * A[i] -1
                res %= mod
            else:
                res += base * A[i] 
                res %= mod
        else:
            base -= iM
            base %= mod
            if M-(A[i]-1) <= (M-special-tmp)%M < M or (M-special-tmp)%M == 0:
                res += base * A[i] +1
                res %= mod
            else:
                res += base * A[i] 
                res %= mod
            
        tmp = (-A[i]+tmp) % M

print(res)
0