peti.cpp

#include <bits/stdc++.h>

using namespace std;

typedef pair<int, int> pii;
typedef long long ll;
const int mn = 1e5 + 10;
const ll mod = 998244353;
int b[mn], c[mn], n, m;

vector<vector<int> > path;
vector<vector<int> > cycle;

bool incyc[mn];
pii loc[mn];
bool vis[mn];
bool ts[mn];
int hd;

void dfs(int x)
{
    vis[x] = ts[x] = 1;
    if (ts[c[x]])
        hd = c[x], cycle.push_back({});
    else if (!vis[c[x]]) {
        dfs(c[x]);
    }
    if (hd) {
        cycle[cycle.size() - 1].push_back(x);
        loc[x] = { cycle.size() - 1, cycle[cycle.size() - 1].size() - 1 };
        incyc[x] = 1;
    }
    if (hd == 0) {
        if (incyc[c[x]])
            path.push_back({ c[x], x });
        else
            path[loc[c[x]].first].push_back(x);
        loc[x] = { path.size() - 1, path[path.size() - 1].size() - 1 };
    }
    if (x == hd)
        hd = 0;
    ts[x] = 0;
}
int main()
{
    int i;
    scanf("%d%d", &n, &m);
    for (i = 1; i <= m; i++)
        scanf("%d", b + i), c[i] = i;
    for (i = 1; i <= m; i++)
        c[b[i]] = c[i];
    for (i = 1; i <= m; i++)
        c[i]++;
    c[m + 1] = m + 1;
    for (i = 1; i <= m; i++)
        if (!vis[i])
            dfs(i);
    ll C, cur = 1, ans = 0;
    scanf("%lld", &C);
    for (i = 1; i <= n; i++) {
        ll v;
        cur = cur * C % mod;
        int st = 1, rem = min(i, n - m + 1);
        if (i > n - m)
            st = i - (n - m);
        if (incyc[st])
            v = cycle[loc[st].first][(loc[st].second - rem + cycle[loc[st].first].size() * 1000000LL) % cycle[loc[st].first].size()];
        else if (i <= loc[st].second)
            v = path[loc[st].first][loc[st].second - rem];
        else {
            rem -= loc[st].second;
            st = path[loc[st].first][0];
            if (st == m + 1)
                v = m + rem;
            else
                v = cycle[loc[st].first][(loc[st].second - rem + cycle[loc[st].first].size() * 1000000LL) % cycle[loc[st].first].size()];
        }
        ans = (ans + (v - 1) * cur) % mod;
    }
    if (ans < 0)
        ans += mod;
    printf("%lld", ans);
}