【HDU】3923 Invoker

同【POJ】2409 Let it Bead

只不过要求逆元。

 1 #include<cstdio>

 2 typedef long long LL;

 3 #define MOD 1000000007

 4 LL PowMod(LL a, LL b, LL c) {

 5     LL ans;

 6     a %= c;

 7     for (ans = 1; b; b >>= 1) {

 8         if (b & 1) {

 9             ans *= a;

10             ans %= c;

11         }

12         a *= a;

13         a %= c;

14     }

15     return ans;

16 }

17 int GCD(int x, int y) {

18     return y ? GCD(y, x % y) : x;

19 }

20 int ExtGcd(int a, int b, int &x, int &y) {

21     int t, d;

22     if (b == 0) {

23         x = 1;

24         y = 0;

25         return a;

26     }

27     d = ExtGcd(b, a % b, x, y);

28     t = x;

29     x = y;

30     y = t - a / b * y;

31     return d;

32 }

33 int InvMod(int a, int n) {

34     int x, y;

35     ExtGcd(a, n, x, y);

36     return (x % n + n) % n;

37 }

38 int main() {

39     int c, ca = 1;

40     int n, i, k;

41     LL ans;

42     scanf("%d", &c);

43     while (c--) {

44         scanf("%d%d", &k, &n);

45         ans = 0;

46         for (i = 1; i <= n; i++) {

47             ans += PowMod(k, GCD(n, i), MOD);

48             ans %= MOD;

49         }

50         if (n & 1) {

51             ans += PowMod(k, (n + 1) >> 1, MOD) * (LL) n % MOD;

52             ans %= MOD;

53         } else {

54             ans += PowMod(k, n >> 1, MOD) * (LL) (n >> 1) % MOD;

55             ans += PowMod(k, (n >> 1) + 1, MOD)

56                     * (LL) (n >> 1)% MOD;

57             ans %= MOD;

58         }

59         printf("Case #%d: %I64d\n", ca++,

60                 ans * InvMod(n << 1, MOD) % MOD);

61     }

62     return 0;

63 }