数学模板

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ma = 

def get_primes(M):
    f = [1]*M
    for i in range(2,isqrt(M)+1):
        if f[i]:
            f[i*i:M:i] = [0] * ((M-1-i*i)//i+1)
    return [i for i in range(2,M) if f[i]]

primes = get_primes(isqrt(ma)+1)

@cache
def factor(x):
    ct = Counter()
    for p in primes:
        while x%p==0:
            x//=p
            ct[p] += 1
    if x>1:
        ct[x] += 1
    return ct

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ma = 
mod = 10**9+7
fac, inv = [1]*(ma+1), [1]*(ma+1)
for i in range(1,ma+1):
    fac[i] = fac[i-1]*i%mod
    inv[i] = pow(fac[i],-1,mod)

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def mpow(mat, n):
	res = mat
	for bit in bin(n)[3:]:
		res = res*res*(mat if bit=='1' else 1)%mod
	return res

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def climb(p,cal):
	eps, step = 1e-7, 1
	while step > eps:
		for i,w in product(range(len(p)),[step,-step]):
			p2 = [a+w*(j==i) for j,a in enumerate(p)]
			if cal(p2)<cal(p):
				p = p2
				break
		else:
			step *= 0.5
	return p