結果

問題 No.1102 Remnants
ユーザー nehan_der_thalnehan_der_thal
提出日時 2020-07-03 22:35:32
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 559 ms / 2,000 ms
コード長 2,628 bytes
コンパイル時間 1,147 ms
コンパイル使用メモリ 81,704 KB
実行使用メモリ 192,596 KB
最終ジャッジ日時 2023-10-17 05:37:38
合計ジャッジ時間 16,444 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge11
このコードへのチャレンジ（β）

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 444 ms
151,744 KB
testcase_01 AC 448 ms
151,744 KB
testcase_02 AC 447 ms
151,760 KB
testcase_03 AC 447 ms
151,752 KB
testcase_04 AC 446 ms
151,756 KB
testcase_05 AC 521 ms
188,104 KB
testcase_06 AC 460 ms
155,168 KB
testcase_07 AC 559 ms
184,412 KB
testcase_08 AC 453 ms
152,008 KB
testcase_09 AC 455 ms
152,008 KB
testcase_10 AC 452 ms
152,004 KB
testcase_11 AC 455 ms
152,028 KB
testcase_12 AC 460 ms
152,036 KB
testcase_13 AC 455 ms
152,024 KB
testcase_14 AC 489 ms
169,364 KB
testcase_15 AC 485 ms
164,876 KB
testcase_16 AC 536 ms
191,012 KB
testcase_17 AC 546 ms
190,488 KB
testcase_18 AC 549 ms
192,400 KB
testcase_19 AC 482 ms
163,556 KB
testcase_20 AC 460 ms
152,760 KB
testcase_21 AC 509 ms
174,908 KB
testcase_22 AC 531 ms
186,260 KB
testcase_23 AC 509 ms
176,236 KB
testcase_24 AC 492 ms
167,788 KB
testcase_25 AC 545 ms
192,596 KB
testcase_26 AC 459 ms
152,008 KB
testcase_27 AC 473 ms
159,864 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 # 

MOD = 10**9+7
k = 72
kk = k // 4
K = 1<<k
nu = lambda L: int("".join([hex(K+a)[3:] for a in L[::-1]]), 16)
st = lambda n: hex(n)[2:]
li = lambda s, l, r: [int(a, 16) % P if len(a) else 0 for a in [s[-(i+1)*kk:-i*kk] for i in range(l, r)]]

def grow(d, v, h):
    h += [0] * d
    f = [(-1 if (i+d) % 2 else 1) * fainv[i] * fainv[d-i] % P * h[i] % P for i in range(d+1)]
    nuf = nu(f)
    a = d * inv[v] % P
    t = [1] * (3*d+3)
    for i in range(1, 3*d+3): t[i] = t[i-1] * (a - d + i - 1) % P
    ti = [1] * (3*d+3)
    ti[-1] = pow(t[-1], P-2, P)
    for i in range(1, 3*d+3)[::-1]: ti[i-1] = ti[i] * (a - d + i - 1) % P
    iv = [1] * (3*d+3)
    for i in range(1, 3*d+3):
        iv[i] = ti[i] * t[i-1] % P

    ###
    g = [inv[i] for i in range(1, 2*d+2)]
    fg = li(st(nuf * nu(g)), d, d * 2 + 1)
    for i in range(d):
        h[i+d+1] = fg[i] * fa[d+i+1] % P * fainv[i] % P

    ###
    g = [iv[i] for i in range(1, 2*d+2)]
    fg = li(st(nuf * nu(g)), d, d * 2 + 1)
    for i in range(d+1):
        h[i] = h[i] * (fg[i] * t[d+i+1] % P * ti[i] % P) % P

    ###
    g = [iv[i] for i in range(d+2, 3*d+3)]
    fg = li(st(nuf * nu(g)), d, d * 2 + 1)
    for i in range(d):
        h[i+d+1] = h[i+d+1] * (fg[i] * t[2*d+i+2] % P * ti[d+i+1] % P) % P

    return h

# Create a table of the factorial of the first v+2 multiples of v, i.e., [0!, v!, 2v!, ..., (v(v+1))!]
def create_table(v):
    s = 1
    X = [1, v+1]
    while s < v:
        X = grow(s, v, X)
        s *= 2

    table = [1]
    for x in X:
        table.append(table[-1] * x % P)
    return table

def fact(i, table):
    a = table[i//v]
    for j in range(i//v*v+1, i+1):
        a = a * j % P
    return a

P = 10**9+7

N = 10**8
v = 1 << (N.bit_length() + 1) // 2
fa = [1] * (2*v+2)
fainv = [1] * (2*v+2)
for i in range(2*v+1):
    fa[i+1] = fa[i] * (i+1) % P
fainv[-1] = pow(fa[-1], P-2, P)
for i in range(2*v+1)[::-1]:
    fainv[i] = fainv[i+1] * (i+1) % P
inv = [0] * (2*v+2)
for i in range(1, 2*v+2):
    inv[i] = fainv[i] * fa[i-1] % P

T = create_table(v)
C = lambda n, k: fact(n, T) * pow(fact(k, T) * fact(n-k, T), P-2, P) % P

inverse = [0, 1]
g1 = [1, 1]
g2 = [1, 1]
for i in range( 2, 3*10**5 + 1 ):
    g1.append( ( g1[-1] * i ) % MOD )
    inverse.append( ( -inverse[MOD % i] * (MOD//i) ) % MOD )
    g2.append( (g2[-1] * inverse[-1]) % MOD )

# 
N, M = map(int, input().split())
X = list(map(int, input().split()))
#print(len(fa), fa[:10])
#
aa = fact(M, T)
Y = [aa]
for i in range(N-1):
    Y.append(Y[-1]*(M+i+1)%MOD)
iM = pow(aa, P-2, P)
R = 0
for i in range(N):
    R = (R + X[i]*Y[i]*Y[N-i-1]*iM*iM*g2[i]*g2[N-i-1]) % P
print(R)
0