求逆元和组合数模板

$O(n)$求逆元

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ll inv[maxn];
inv[1] = 1;
rep(i,2,maxn)
inv[i] = inv[mod%i] * (mod-mod/i) % mod;

$O(n)$求阶乘

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ll f[maxn];
ll f[1] = 1;
rep(i,2,maxn)
f[i] = f[i-1]*i;

求$nchoose k$

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ll cur,p[maxn],q[maxn],inv[maxn];
ll (ll n,ll k){
return p[n]*q[k]%mod*q[n-k]%mod;
}
ll c(ll n,ll k){
if(n<maxn) return C(n,k);
if(!k) return 1;
return cur = cur*inv[k]%mod*((n-k+1)%mod)%mod;
}
void init(){
p[0]=p[1]=q[0]=q[1]=inv[0]=inv[1]=1;
for(ll i = 2;i<maxn;i++){
inv[i] = (mod-mod/i)*inv[mod%i]%mod;
q[i] = q[i-1] * inv[i] % mod;
p[i] = p[i-1] * i % mod;
}
}

求$A^k_n$

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int A(int n,int k){
return c(n,k)*p[k]%mod;
}