3696. The Luckiest number

23422872

POJ/3696/3696.cpp

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+#include <algorithm>
+#include <iostream>
+#include <limits>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+int t;
+long long l;
+
+long long euler(long long x) {
+    long long r = x;
+    for (long long i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            r = r / i * (i - 1);
+            while (x % i == 0) x /= i;
+        }
+    }
+    if (x > 1) r = r / x * (x - 1);
+    return r;
+}
+
+long long binmul(long long a, long long b, long long m) {
+    unsigned long long c =
+        (unsigned long long)a * b -
+        (unsigned long long)((long double)a / m * b + 0.5L) * m;
+    if (c < m) return c;
+    return c + m;
+}
+
+long long binpow(long long a, long long b, long long m) {
+    a %= m;
+    long long res = 1;
+    while (b > 0) {
+        if (b & 1) res = binmul(res, a, m);
+        a = binmul(a, a, m);
+        b >>= 1;
+    }
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+
+    while (cin >> l, l) {
+        long long d = std::__gcd(l, 8ll);
+        long long n = euler(9ll * l / d);
+        long long ans = std::numeric_limits<long long>::max();
+
+        for (long long i = 1; i * i <= n; i++) {
+            if (n % i == 0) {
+                if (binpow(10, i, 9ll * l / d) == 1) ans = std::min(ans, i);
+                if (binpow(10, n / i, 9ll * l / d) == 1) ans = std::min(ans, n / i);
+            }
+        }
+
+        cout << "Case " << ++t << ": " << (ans == std::numeric_limits<long long>::max() ? 0 : ans) << endl;
+    }
+
+    return 0;
+}