Signal Processing

                                #include "bits/stdc++.h"
using namespace std;
#define pii pair<int,int>
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define ll long long

//<============FFT Starts=============>\\

const int N = 2e5 + 9;

const double PI = acos(-1);
struct base {
    double a, b;
    base(double a = 0, double b = 0) : a(a), b(b) {}
    const base operator + (const base &c) const
        { return base(a + c.a, b + c.b); }
    const base operator - (const base &c) const
        { return base(a - c.a, b - c.b); }
    const base operator * (const base &c) const
        { return base(a * c.a - b * c.b, a * c.b + b * c.a); }
};
void fft(vector<base> &p, bool inv = 0) {
    int n = p.size(), i = 0;
    for(int j = 1; j < n - 1; ++j) {
        for(int k = n >> 1; k > (i ^= k); k >>= 1);
        if(j < i) swap(p[i], p[j]);
    }
    for(int l = 1, m; (m = l << 1) <= n; l <<= 1) {
        double ang = 2 * PI / m;
        base wn = base(cos(ang), (inv ? 1. : -1.) * sin(ang)), w;
        for(int i = 0, j, k; i < n; i += m) {
            for(w = base(1, 0), j = i, k = i + l; j < k; ++j, w = w * wn) {
                base t = w * p[j + l];
                p[j + l] = p[j] - t;
                p[j] = p[j] + t;
            }
        }
    }
    if(inv) for(int i = 0; i < n; ++i) p[i].a /= n, p[i].b /= n;
}
vector<long long> multiply(vector<int> &a, vector<int> &b) {
    int n = a.size(), m = b.size(), t = n + m - 1, sz = 1;
    while(sz < t) sz <<= 1;
    vector<base> x(sz), y(sz), z(sz);
    for(int i = 0 ; i < sz; ++i) {
        x[i] = i < (int)a.size() ? base(a[i], 0) : base(0, 0);
        y[i] = i < (int)b.size() ? base(b[i], 0) : base(0, 0);
    }
    fft(x), fft(y);
    for(int i = 0; i < sz; ++i) z[i] = x[i] * y[i];
    fft(z, 1);
    vector<long long> ret(sz);
    for(int i = 0; i < sz; ++i) {
        if( z[i].a>=0 )
            ret[i] = (long long) (z[i].a + 0.5);
        else
            ret[i] = (long long) (z[i].a - 0.5);
    }
    while((int)ret.size() > 1 && ret.back() == 0) ret.pop_back();
    return ret;
}


//<============FFT Ends=============>\\

int main(){

    int n,m;
    cin>>n>>m;

    vector<int> a,b;
    a.resize(n,0);
    b.resize(m,0);

    for(int i=0;i<n;i++)cin>>a[i];
    for(int i=0;i<m;i++){
        int v;
        cin>>v;
        b[m-i-1] = v;
    }



    vector<ll> c = multiply(a,b);
    //c.resize(2*n-1,0);
    for(int i=0;i<c.size();i++){
        cout<<c[i]<<" ";
    }
    for(int i=c.size();i<n-m-1;i++) cout<<"0 ";

}