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source/Math/general_lucas.cpp

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+vector<ll> euler(1000003, -1), primes; 
+//Generate primes and also calculate the euler number 
+void genprime() { 
+ 	for(ll i = 2;i<=1000002;i++) { 
+ 		if(euler[i]==-1) { 
+ 			primes.push_back(i); 
+ 			euler[i] = i-1; 
+ 			for(ll j = 2*i; j<=1000002; j+=i) { 
+ 				if(euler[j]==-1)euler[j] = j; 
+ 				euler[j] = (euler[j]/i)*(i-1); 
+ 			} 
+ 		} 
+ 	} 
+} 
+//Calculates x raised to the power of p % m 
+ll powll(ll x, ll p, ll m = 1ll<<62) 
+// Mod inverse
+ll inverse(ll x, ll m) 
+ 
+//finds (n!)_p 
+ll ff(ll n, ll p, ll q) 
+{ 
+    ll x = 1, y = powll(p, q); 
+    for(ll i = 2; i<=n;i++) if(i%p) 
+        x = (x*i)%y; 
+    return x%y; 
+} 
+  
+//Generalized Lucas Theorem calculates nCm mod p^q 
+ll lucas_pow_comb(ll n, ll m, ll p, ll q) { 
+ 	ll r = n-m, x = powll(p, q); 
+ 	ll e0 = 0, eq = 0; 
+ 	ll mul = (p==2&&q>=3)? 1: -1; 
+ 	ll cr = r, cm = m, carry = 0, cnt = 0; 
+ 	while(cr||cm||carry)  { 
+ 		cnt++; 
+ 		int rr = cr%p, rm = cm%p; 
+ 		if(rr + rm + carry >= p) { 
+ 			e0++; 
+ 			if(cnt>=q)eq++; 
+ 		} 
+ 		carry = (carry+rr+rm)/p; 
+ 		cr/=p; cm/=p; 
+ 	} 
+ 	mul = powll(p, e0)*powll(mul, eq); 
+ 	ll ret = (mul % x + x) % x; 
+ 	ll temp = 1; 
+ 	for(ll i = 0;;i++)//This is THE line that calculates the formula { 
+ 		ret = ((ret*ff((n/temp)%x, p, q)%x)%x*(inverse(ff((m/temp)%x, p, q), x)%x*inverse(ff((r/temp)%x, p, q), x)%x)%x)%x; 
+  
+ 		if(temp>n/p && temp>m/p && temp>r/p) 
+			break; 
+ 		temp = temp*p; 
+ 	} 
+ 	return (ret%x+x)%x; 
+}