Solved beautiful numbers

a2oj/1899-rating/beautiful_numbers.cpp

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+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define p 1000000007
+
+typedef long long ll;
+
+long long power(long long x, long long y) {
+    long long res = 1;      // Initialize result
+
+    x = x % p;  // Update x if it is more than or
+                // equal to p
+
+    while (y > 0)
+    {
+        // If y is odd, multiply x with result
+        if (y & 1)
+            res = (res*x) % p;
+
+        // y must be even now
+        y = y>>1; // y = y/2
+        x = (x*x) % p;
+    }
+    return res%p;
+}
+
+long long gcdExtended(long long a, long long b, long long *x, long long *y)
+{
+    // Base Case
+    if (a == 0)
+    {
+        *x = 0, *y = 1;
+        return b;
+    }
+
+    long long x1, y1; // To store results of recursive call
+    long long gcd = gcdExtended(b%a, a, &x1, &y1);
+
+    // Update x and y using results of recursive
+    // call
+    *x = y1 - (b/a) * x1;
+    *y = x1;
+
+    return gcd;
+}
+
+long long modInverse(long long b)
+{
+    long long x, y; // used in extended GCD algorithm
+    long long g = gcdExtended(b, p, &x, &y);
+
+    // Return -1 if b and m are not co-prime
+    if (g != 1)
+        return -1;
+
+    // m is added to handle negative x
+    return (x%p + p) % p;
+}
+
+// a/b
+long long mod_divide(long long a, long long b) {
+   a = a % p;
+   long long inv = modInverse(b);
+   return (inv * a) % p;
+}
+
+// a*b
+long long mulmod(long long a, long long b) {
+   long long res = 0;
+   a = a % p;
+   while (b > 0) {
+      if (b % 2 == 1) {
+         res = (res + a) % p;
+      }
+      a = (a*2)%p;
+      b /= 2;
+   }
+   return res%p;
+}
+
+long long choose(long long n, long long b) {
+   long long ans = 1;
+   long long fact = 1;
+   for (long long i = 0; i < b; ++i) {
+      ans = mulmod(ans, n - i);;
+      fact = mulmod(fact, i + 1);
+   }
+   return mod_divide(ans, fact);
+}
+
+
+int a, b, n;
+
+bool is_good(int num) {
+    while (num > 0) {
+        if (num % 10 != a && num % 10 != b) {
+            return false;
+        }
+        num = num / 10;
+    }
+    return true;
+}
+
+int main() {
+    cin >> a >> b >> n;
+    ll choose = 1;
+    ll ans = 0;
+    for (int i = 0; i <= n; ++i) {
+        if (is_good(a*i + (n - i)*b)) {
+            ans = (ans + choose) % p;
+        }
+        choose = mod_divide(mulmod(choose, (n - i)), (i + 1));
+    }
+    cout << ans << endl;
+}