WPUMPS (CSPTST 2022-2023)

#define task "WPUMPS"
#include <iostream>
#include <cstdio>

using namespace std;

using ll = long long;
using ld = long double;

constexpr int N = 3e3 + 5;
constexpr ll mod = 1e9 + 7;
int n, m;
ll a[N], b[N];
ll rgt[N];

void Read()
{
    cin >> n;

    for (int i = 1; i <= n; ++i)
        cin >> a[i];

    cin >> m;
}

ll C(int k, int n)
{
    if (k > n)
        return 0;

    ll ans = rgt[k];

    for (int i = 0; i < k; ++i)
        ans = ans * (n - i) % mod;

    return ans;
}

ll Cal(int m, int n)
{
    return C(min(n - 1, m - 1), m + n - 2);
}

ll Pow(ll a, ll b)
{
    ll ans(1);

    for (; b; b >>= 1)
    {
        if (b & 1)
            ans = ans * a % mod;
        a = a * a % mod;
    }

    return ans;
}

void Solve()
{
    rgt[0] = 1;

    for (int i = 1; i <= n + 1; ++i)
        rgt[i] = rgt[i - 1] * Pow(i, mod - 2) % mod;

    for (int i = 1; i <= n; ++i)
    {
        ll v = Cal(m, i);

        for (int j = 1; j + i - 1 <= n; ++j)
            (b[j + i - 1] += a[j] * v) %= mod;
    }

    for (int i = 1; i <= n; ++i)
        cout << b[i] << " ";
}

int32_t main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    if (fopen(task ".INP", "r"))
    {
        freopen(task ".INP", "r", stdin);
        freopen(task ".OUT", "w", stdout);
    }

    Read();
    Solve();
}