#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define popcount __builtin_popcount using namespace std; typedef long long int ll; typedef pair P; const ll MOD=1<<20; ll powmod(ll a, ll k){ ll ap=a, ans=1; while(k){ if(k&1){ ans*=ap; ans%=MOD; } ap=ap*ap; ap%=MOD; k>>=1; } return ans; } ll inv(ll a){ return powmod(a, MOD/2-1); } ll f[2000001], invf[2000001]; int fe[2000001]; void fac(int n){ f[0]=invf[0]=1; for(ll i=1; i<=n; i++){ int e=0; ll x=i; while(x%2==0){ x/=2; e++; } f[i]=f[i-1]*x%MOD; fe[i]=fe[i-1]+e; invf[i]=inv(f[i]); } } ll comb(int x, int y){ if(!(0<=y && y<=x)) return 0; int e=fe[x]-fe[y]-fe[x-y]; if(e>=20) return 0; return f[x]*invf[y]%MOD*invf[x-y]%MOD*(1ll<