//a_N = 1 + 100 + 100^2 + … + 100^(N-1) = (100^N - 1) / 99 //10^9 + 7で割った余り…フェルマーの小定理より(100^N - 1) * 99^(10^9 + 5) % (10^9 + 7)と値が一致 //a_11で割った余り…N % 11 == 0のとき0より、a_N % a_11 = a_(N % 11) #include #define int long long using namespace std; int powmod(int a, int n, int mod) { if (n == 0) return 1; if (n % 2 == 0) return powmod((a * a) % mod, n / 2, mod) % mod; return (a * powmod(a, n - 1, mod)) % mod; } signed main() { int n; cin >> n; int p = 1000000007; int a = (powmod(100, n, p) + p - 1) % p; int b = powmod(99, p - 2, p); cout << (a * b) % p << endl; int ans = 0, add = 1; for (int i = 0; i < n % 11; i++) { ans += add; add *= 100; } cout << ans << endl; return 0; }