結果
| 問題 |
No.8046 yukicoderの過去問
|
| コンテスト | |
| ユーザー |
 Eki1009
|
| 提出日時 | 2020-11-04 01:25:59 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 15,445 bytes |
| コンパイル時間 | 873 ms |
| コンパイル使用メモリ | 82,560 KB |
| 実行使用メモリ | 184,272 KB |
| 最終ジャッジ日時 | 2024-07-22 09:30:12 |
| 合計ジャッジ時間 | 10,689 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 4 WA * 5 |
ソースコード
mod = 1000000007
MOD1 = 167772161
MOD2 = 469762049
MOD3 = 754974721
sum_e1 = (65249968, 137365239, 35921276, 103665800, 89728614, 164955302, 108901219, 163950188, 113252399, 166581688, 59783366, 95476790, 130818126, 39440948, 65800545, 14559656, 3285286, 36462062, 164082627, 9320421, 66343657, 69024390, 38289678)
sum_ie1 = (102522193, 71493608, 26998229, 133555027, 128975965, 16363816, 145463520, 130828795, 26375299, 18078794, 87407453, 28151929, 49401241, 112914531, 118959329, 68815302, 71865958, 21459372, 44393528, 43709352, 30681399, 153195333, 141748999)
sum_e2 = (450151958, 26623616, 25192837, 305390008, 399060560, 78724413, 312251397, 151088193, 437503217, 339869829, 197503427, 460844482, 64795813, 392699793, 323591778, 435162849, 324666788, 397071166, 191521520, 39442863, 102932772, 52822010, 231589706, 155147527)
sum_ie2 = (19610091, 129701348, 104677229, 445839763, 375500824, 451642859, 145445927, 77724141, 367250623, 54456563, 257713867, 444918711, 335270416, 371371281, 307213086, 452878044, 243328637, 152011944, 315423951, 456185089, 218081060, 136058803, 203260256, 412215962)
sum_e3 = (323860177, 709730407, 436702940, 377572811, 498550177, 265767825, 100966039, 179671739, 669698534, 133401683, 473130419, 31725267, 490947959, 457689220, 238049902, 49087920, 531104465, 448493484, 262339740, 717535334, 230862726, 416349974)
sum_ie3 = (431114544, 205430076, 560644912, 287842920, 662221072, 3742006, 250769401, 512611432, 114808946, 480642746, 472385404, 152834416, 131937947, 932118, 246823069, 305783701, 453008707, 746618366, 510123862, 69538303, 659667489, 259138136)
I_li = []
def extgcd(s, t):
sx, sy = 1, 0
tx, ty = 0, 1
while s % t:
temp = s // t
s, t = t, s - t * temp
sx, tx = tx, sx - tx * temp
sy, ty = ty, sy - ty * temp
return tx, ty
def invmod(s):
x, y = extgcd(s, mod)
return x%mod
def butterfly1(arr):
n = len(arr)
h = (n - 1).bit_length()
for ph in range(1, h + 1):
w = 1 << (ph - 1)
p = 1 << (h - ph)
now = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p] * now
arr[i + offset] = (l + r) % MOD1
arr[i + offset + p] = (l - r) % MOD1
now *= sum_e1[(~s & -~s).bit_length() - 1]
now %= MOD1
def butterfly_inv1(arr):
n = len(arr)
h = (n - 1).bit_length()
for ph in range(1, h + 1)[::-1]:
w = 1 << (ph - 1)
p = 1 << (h - ph)
inow = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p]
arr[i + offset] = (l + r) % MOD1
arr[i + offset + p] = (MOD1 + l - r) * inow % MOD1
inow *= sum_ie1[(~s & -~s).bit_length() - 1]
inow %= MOD1
def convolution1(a, b):
n = len(a)
m = len(b)
if not n or not m: return []
if min(n, m) <= 100:
if n < m:
n, m = m, n
a, b = b, a
res = [0] * (n + m - 1)
for i in range(n):
for j in range(m):
res[i + j] += a[i] * b[j]
res[i + j] %= MOD1
return res
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
b += [0] * (z - m)
butterfly1(a)
butterfly1(b)
for i in range(z):
a[i] *= b[i]
a[i] %= MOD1
butterfly_inv1(a)
a = a[:n + m - 1]
iz = pow(z, MOD1 - 2, MOD1)
for i in range(n + m - 1):
a[i] *= iz
a[i] %= MOD1
return a
def autocorrelation1(a):
n = len(a)
if not n: return []
if n <= 100:
res = [0] * (2 * n - 1)
for i in range(n):
for j in range(n):
res[i + j] += a[i] * a[j]
res[i + j] %= MOD1
return res
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
butterfly1(a)
for i in range(z):
a[i] *= a[i]
a[i] %= MOD1
butterfly_inv1(a)
a = a[:2 * n - 1]
iz = pow(z, MOD1 - 2, MOD1)
for i in range(2 * n - 1):
a[i] *= iz
a[i] %= MOD1
return a
def butterfly2(arr):
n = len(arr)
h = (n - 1).bit_length()
for ph in range(1, h + 1):
w = 1 << (ph - 1)
p = 1 << (h - ph)
now = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p] * now
arr[i + offset] = (l + r) % MOD2
arr[i + offset + p] = (l - r) % MOD2
now *= sum_e2[(~s & -~s).bit_length() - 1]
now %= MOD2
def butterfly_inv2(arr):
n = len(arr)
h = (n - 1).bit_length()
for ph in range(1, h + 1)[::-1]:
w = 1 << (ph - 1)
p = 1 << (h - ph)
inow = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p]
arr[i + offset] = (l + r) % MOD2
arr[i + offset + p] = (MOD2 + l - r) * inow % MOD2
inow *= sum_ie2[(~s & -~s).bit_length() - 1]
inow %= MOD2
def convolution2(a, b):
n = len(a)
m = len(b)
if not n or not m: return []
if min(n, m) <= 100:
if n < m:
n, m = m, n
a, b = b, a
res = [0] * (n + m - 1)
for i in range(n):
for j in range(m):
res[i + j] += a[i] * b[j]
res[i + j] %= MOD2
return res
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
b += [0] * (z - m)
butterfly2(a)
butterfly2(b)
for i in range(z):
a[i] *= b[i]
a[i] %= MOD2
butterfly_inv2(a)
a = a[:n + m - 1]
iz = pow(z, MOD2 - 2, MOD2)
for i in range(n + m - 1):
a[i] *= iz
a[i] %= MOD2
return a
def autocorrelation2(a):
n = len(a)
if not n: return []
if n <= 100:
res = [0] * (2 * n - 1)
for i in range(n):
for j in range(n):
res[i + j] += a[i] * a[j]
res[i + j] %= MOD2
return res
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
butterfly2(a)
for i in range(z):
a[i] *= a[i]
a[i] %= MOD2
butterfly_inv2(a)
a = a[:2 * n - 1]
iz = pow(z, MOD2 - 2, MOD2)
for i in range(2 * n - 1):
a[i] *= iz
a[i] %= MOD2
return a
def butterfly3(arr):
n = len(arr)
h = (n - 1).bit_length()
for ph in range(1, h + 1):
w = 1 << (ph - 1)
p = 1 << (h - ph)
now = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p] * now
arr[i + offset] = (l + r) % MOD3
arr[i + offset + p] = (l - r) % MOD3
now *= sum_e3[(~s & -~s).bit_length() - 1]
now %= MOD3
def butterfly_inv3(arr):
n = len(arr)
h = (n - 1).bit_length()
for ph in range(1, h + 1)[::-1]:
w = 1 << (ph - 1)
p = 1 << (h - ph)
inow = 1
for s in range(w):
offset = s << (h - ph + 1)
for i in range(p):
l = arr[i + offset]
r = arr[i + offset + p]
arr[i + offset] = (l + r) % MOD3
arr[i + offset + p] = (MOD3 + l - r) * inow % MOD3
inow *= sum_ie3[(~s & -~s).bit_length() - 1]
inow %= MOD3
def convolution3(a, b):
n = len(a)
m = len(b)
if not n or not m: return []
if min(n, m) <= 100:
if n < m:
n, m = m, n
a, b = b, a
res = [0] * (n + m - 1)
for i in range(n):
for j in range(m):
res[i + j] += a[i] * b[j]
res[i + j] %= MOD3
return res
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
b += [0] * (z - m)
butterfly3(a)
butterfly3(b)
for i in range(z):
a[i] *= b[i]
a[i] %= MOD3
butterfly_inv3(a)
a = a[:n + m - 1]
iz = pow(z, MOD3 - 2, MOD3)
for i in range(n + m - 1):
a[i] *= iz
a[i] %= MOD3
return a
def autocorrelation3(a):
n = len(a)
if not n: return []
if n <= 100:
res = [0] * (2 * n - 1)
for i in range(n):
for j in range(n):
res[i + j] += a[i] * a[j]
res[i + j] %= MOD3
return res
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
butterfly2(a)
for i in range(z):
a[i] *= a[i]
a[i] %= MOD3
butterfly_inv2(a)
a = a[:2 * n - 1]
iz = pow(z, MOD3 - 2, MOD3)
for i in range(2 * n - 1):
a[i] *= iz
a[i] %= MOD3
return a
def inv_gcd(a, b):
a %= b
if a == 0: return b, 0
s = b
t = a
m0 = 0
m1 = 1
while t:
u = s // t
s -= t * u
m0 -= m1 * u
s, t = t, s
m0, m1 = m1, m0
if m0 < 0: m0 += b // s
return s, m0
def crt(r, m):
assert len(r) == len(m)
n = len(r)
r0 = 0
m0 = 1
for i in range(n):
assert 1 <= m[i]
r1 = r[i] % m[i]
m1 = m[i]
if m0 < m1:
r0, r1 = r1, r0
m0, m1 = m1, m0
if m0 % m1 == 0:
if r0 % m1 != r1: return 0, 0
continue
g, im = inv_gcd(m0, m1)
u1 = m1 // g
if (r1 - r0) % g: return 0, 0
x = (r1 - r0) // g * im % u1
r0 += x * m0
m0 *= u1
if (r0 < 0): r0 += m0
return r0, m0
def convolution(a, b):
n = len(a)
m = len(b)
c1 = convolution1(a.copy(), b.copy())[:n + m - 1]
c2 = convolution2(a.copy(), b.copy())[:n + m - 1]
c3 = convolution3(a.copy(), b.copy())[:n + m - 1]
res = [0] * (n + m - 1)
for i, v in enumerate(zip(c1, c2, c3)):
cr, cm = crt(v, (MOD1, MOD2, MOD3))
res[i] += cr
res[i] %= mod
return res
def autocorrelation(a):
n = len(a)
a1 = autocorrelation1(a.copy())[:2 * n - 1]
a2 = autocorrelation2(a.copy())[:2 * n - 1]
a3 = autocorrelation3(a.copy())[:2 * n - 1]
res = [0] * (2 * n - 1)
for i, v in enumerate(zip(a1, a2, a3)):
cr, cm = crt(v, (MOD1, MOD2, MOD3))
res[i] += cr
res[i] %= mod
return res
class formal_power_series:
def __init__(self, poly, deg=2*10**5):
self.poly = [p % mod for p in poly[:deg + 1]]
self.deg = deg
def __getitem__(self, key):
if key < 0:
raise IndexError("list index out of range")
if key >= len(self.poly):
return 0
else:
return self.poly[key]
def __setitem__(self, key, value):
if key < 0:
raise IndexError("list index out of range")
if key >= len(self.poly):
if key > self.deg:
return
self.poly += [0] * (key - len(self.poly) + 1)
self.poly[key] = value % mod
def times(self, n):
n %= mod
res = [p * n for p in self.poly]
return formal_power_series(res, self.deg)
def truncate(self, n):
res = self.poly[:n]
return formal_power_series(res, self.deg)
def __pos__(self):
return self
def __neg__(self):
return self.times(-1)
def __add__(self, other):
if other.__class__ == formal_power_series:
s = len(self.poly)
t = len(other.poly)
n = min(s, t)
m = min(self.deg, other.deg)
res = [self.poly[i] + other.poly[i] for i in range(n)]
if s >= t:
res += self.poly[t:]
else:
res += other.poly[s:]
return formal_power_series(res, m)
else:
self.poly[0] += other
self.poly[0] %= mod
return self
def __radd__(self, other):
return self + other
def __sub__(self, other):
return self + (-other)
def __rsub__(self, other):
return (-self) + other
def __mul__(self, other):
if other.__class__ == formal_power_series:
m = min(self.deg, other.deg)
res = convolution(self.poly.copy(), other.poly.copy())
return formal_power_series(res, m)
else:
return self.times(other)
def __rmul__(self, other):
return self.times(other)
def square(self):
res = autocorrelation(self.poly.copy())
return formal_power_series(res, self.deg)
def inv(self):
r = invmod(self.poly[0])
m = 1
res = formal_power_series([r], self.deg)
while m <= self.deg:
m <<= 1
t_li = (self.truncate(m) * res.square().truncate(m)).truncate(m)
res = res * 2 - t_li
return res
def __truediv__(self, other):
if other.__class__ == formal_power_series:
return self * other.inv()
else:
return self * invmod(other)
def __rtruediv__(self, other):
return other * self.inv()
def __floordiv__(self, other):
if other.__class__ == formal_power_series:
return self * other.inv()
else:
return self * invmod(other)
def __rfloordiv__(self, other):
return other * self.inv()
def __mod__(self, other):
return self - (self / other) * other
def differentiate(self):
res = [k * p for k, p in enumerate(self.poly[1:], 1)]
return formal_power_series(res, self.deg)
def integrate(self):
while len(I_li) <= len(self.poly):
I_li.append(invmod(len(I_li)))
res = [0] + [I_li[k] * p for k, p in enumerate(self.poly, 1)]
return formal_power_series(res, self.deg)
def log(self):
return (self.differentiate() / self).integrate()
def exp(self):
res = formal_power_series([1], self.deg)
g_li = formal_power_series([1], self.deg)
df = self.differentiate()
m = 1
while m <= self.deg:
g_li = g_li * 2 - (res * g_li.square()).truncate(m)
m <<= 1
dft = df.truncate(m)
w_li = dft + (g_li * (res.differentiate() - (res * dft).truncate(m))).truncate(m)
res += (res * (self.truncate(m) - w_li.integrate().truncate(m))).truncate(m)
return res
def __pow__(self, n):
m = abs(n)
for d, p in enumerate(self.poly):
if p:
break
else:
return formal_power_series([], self.deg)
if d * m >= self.deg + 1:
return formal_power_series([], self.deg)
g_li = formal_power_series(self.poly[d:], self.deg)
g_li = ((g_li * invmod(p)).log() * m).exp() * pow(p, m, mod)
res = formal_power_series([0] * (d * m) + g_li.poly, self.deg)
if n >= 0:
return res
else:
return res.inv()
k = int(input())
n = int(input())
X = tuple(map(int, input().split()))
F = [0]*(k+1)
F[0] = 1
for x in X:
if x > k:
break
F[x] = -1
P = formal_power_series(F, k)
ans = P.inv()[k]
print(ans)