Create 3405. Count the Number of Arrays with K Matching Adjacent Elem…

3405. Count the Number of Arrays with K Matching Adjacent Elements

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+const int mod=1e9+7;
+class Solution {
+public:
+    static inline long long modPow(long long x, int exp, int Mod=mod){
+        if (exp==0) return 1;
+        int y=(exp&1)?x:1;
+        return modPow(x*x%Mod, exp>>1)*y%Mod;
+    }
+
+    // Euclidean algo finds x, y, d such that ax+by = d where d=gcd(a, b)
+    static inline int modInverse(int a, int b=mod) {//mod is prime d=1
+        int x0 = 1, x1 = 0;
+        int r0 = a, r1 = b;
+        while (r1 != 0) {
+            int q = r0/r1, rr = r1, xx = x1;
+            r1 = r0-q * r1;
+            x1 = x0-q * x1;
+            r0 = rr;
+            x0 = xx;
+        }
+        if (x0 < 0) x0+= b;
+        return x0;
+    }
+    static long long comb(int n, int k){
+        if (n<2*k) return comb(n, n-k);
+        long long denominator=1;
+        for(int i=1; i<=k; i++){
+            denominator*=i;
+            if (denominator>mod) denominator%=mod;
+        }
+        long long ans=modInverse(denominator);
+        for (int i=n; i>=n-k+1; i--){
+            ans*=i;
+            if (ans>mod) ans%=mod;
+        }
+        return ans;
+    }
+    static int countGoodArrays(int n, int m, int k) {
+        return m*modPow(m-1, n-k-1)%mod*comb(n-1, k)%mod;
+
+    }
+};