結果

問題 No.1627 三角形の成立
ユーザー lam6er
提出日時 2025-03-26 15:55:14
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 235 ms / 1,000 ms
コード長 2,272 bytes
コンパイル時間 182 ms
コンパイル使用メモリ 82,600 KB
実行使用メモリ 81,008 KB
最終ジャッジ日時 2025-03-26 15:56:05
合計ジャッジ時間 3,645 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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 * 2
other AC * 22
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 = 10**9 + 7
inv2 = pow(2, MOD - 2, MOD)
def compute_mobius(max_d):
    max_d += 1
    is_prime = [True] * max_d
    mu = [1] * max_d
    min_prime = [0] * max_d
    for i in range(2, max_d):
        if is_prime[i]:
            min_prime[i] = i
            for j in range(i, max_d, i):
                is_prime[j] = False
                if min_prime[j] == 0:
                    min_prime[j] = i
    for i in range(2, max_d):
        if i == 1:
            continue
        p = min_prime[i]
        if p == 0:
            continue
        cnt = 0
        tmp = i
        while tmp % p == 0:
            tmp //= p
            cnt += 1
        if cnt >= 2:
            mu[i] = 0
        else:
            mu[i] = -mu[tmp]
    return mu
n, m = map(int, input().split())
def comb(k):
    if k < 3:
        return 0
    return k * (k - 1) * (k - 2) // 6 % MOD
total = comb(n * m)
horiz = (n * comb(m)) % MOD
vert = (m * comb(n)) % MOD
G = min(n - 1, m - 1) if (n >= 1 and m >= 1) else 0
max_mobius = max(n, m) if G == 0 else max((n - 1) // 1, (m - 1) // 1)
mu = compute_mobius(max_mobius)
c_diag = 0
for g in range(1, G + 1):
    d_max = min((m - 1) // g, (n - 1) // g)
    if d_max < 1:
        continue
    S_g = 0
    for d in range(1, d_max + 1):
        mud = mu[d]
        if mud == 0:
            continue
        gd = g * d
        A = (m - 1) // gd
        B = (n - 1) // gd
        
        sum_a_part1 = (m % MOD) * (A % MOD) % MOD
        sum_a_part2 = (gd % MOD) * (A % MOD) % MOD
        sum_a_part2 = sum_a_part2 * ((A + 1) % MOD) % MOD
        sum_a_part2 = sum_a_part2 * inv2 % MOD
        sum_a = (sum_a_part1 - sum_a_part2) % MOD
        
        sum_b_part1 = (n % MOD) * (B % MOD) % MOD
        sum_b_part2 = (gd % MOD) * (B % MOD) % MOD
        sum_b_part2 = sum_b_part2 * ((B + 1) % MOD) % MOD
        sum_b_part2 = sum_b_part2 * inv2 % MOD
        sum_b = (sum_b_part1 - sum_b_part2) % MOD
        
        term = mud * sum_a % MOD
        term = term * sum_b % MOD
        S_g = (S_g + term) % MOD
    
    contribution = (g - 1) * S_g % MOD
    contribution = contribution * 2 % MOD
    c_diag = (c_diag + contribution) % MOD
collinear = (horiz + vert + c_diag) % MOD
ans = (total - collinear) % MOD
print(ans if ans >= 0 else ans + MOD)
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