⚡ improves binomial mod performance

algorithms/math/binomial-mod.cpp

@@ -1,22 +1,26 @@
 const ll MOD = 1e9 + 7;
-const ll maxn = 2 * 1e6;
-vll fats(maxn + 1, -1);
+const ll MAXN = 1'00'000;
+ll FACT[MAXN + 1];
 void precompute() {
-  fats[0] = 1;
-  for (ll i = 1; i <= maxn; i++) {
-    fats[i] = (fats[i - 1] * i) % MOD;
+  #warning Remember to call precompute before use binommod !
+  FACT[0] = 1;
+  for (ll i = 1; i <= MAXN; i++) {
+    FACT[i] = (FACT[i - 1] * i) % MOD;
   }
 }
 
-ll fpow(ll a, ll n, ll mod = LLONG_MAX) {
-  if (n == 0ll) return 1ll;
-  if (n == 1ll) return a;
-  ll x = fpow(a, n / 2ll, mod) % mod;
-  return ((x * x) % mod * (n & 1ll ? a : 1ll)) % mod;
+ll fpow(ll a, ll k) {
+  ll ret = 1;
+  while (k) {
+    if (k & 1) ret = (ret * a) % MOD;
+    a = (a * a) % MOD;
+    k >>= 1;
+  }
+  return ret;
 }
 
 ll binommod(ll n, ll k) {
-  ll upper = fats[n];
-  ll lower = (fats[k] * fats[n - k]) % MOD;
-  return (upper * fpow(lower, MOD - 2ll, MOD)) % MOD;
+  ll upper = FACT[n];
+  ll lower = (FACT[k] * FACT[n - k]) % MOD;
+  return (upper * fpow(lower, MOD - 2ll)) % MOD;
 }