ll inv[N];
void init(){
inv[1] = inv[0] = 1;
for(int i = 2;i < N;i++)
inv[i] = inv[mod%i]*(mod-mod/i)%mod;
}
ll inv[N];
void init(){
inv[1] = inv[0] = 1;
for(int i = 2;i < N;i++)
inv[i] = inv[mod%i]*(mod-mod/i)%mod;
}