#include #include #include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; template vector> vec2d(int n, int m, T v){ return vector>(n, vector(m, v)); } template vector>> vec3d(int n, int m, int k, T v){ return vector>>(n, vector>(m, vector(k, v))); } template void print_vector(vector v, char delimiter=' '){ if(v.empty()) { cout << endl; return; } for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter; cout << v.back() << endl; } using mint = atcoder::modint; ostream& operator<<(ostream& os, const mint& m){ os << m.val(); return os; } ll mod_pow(ll a, ll n, ll mod) { ll ans = 1; return ans; } mint solve(ll n, ll m, int l, int k, int b){ mint::set_mod(b); vector ans(l), a(l); ans[0] = 1; a[0] = 1; if(l == 1){ a[0] += m; }else{ a[1] = 1; } while (n > 0) { if (n&1) { vector nx(l); for(int i = 0; i < l; i++){ for(int j = 0; j < l; j++){ if(i+j >= l){ nx[(i+j)%l] += ans[i]*a[j]*m; }else{ nx[(i+j)%l] += ans[i]*a[j]; } } } ans = nx; } vector nx(l); for(int i = 0; i < l; i++){ for(int j = 0; j < l; j++){ if(i+j >= l){ nx[(i+j)%l] += a[i]*a[j]*m; }else{ nx[(i+j)%l] += a[i]*a[j]; } } } a = nx; n >>= 1; } return ans[k]; } mint naive(ll n, ll m, int l, int k, int b){ mint::set_mod(b); auto comb = vec2d(n+1, n+1, mint(0)); for(int i = 0; i <= n; i++) { comb[i][0] = 1; for(int j = 1; j <= i; j++){ comb[i][j] = comb[i-1][j]+comb[i-1][j-1]; } } mint ans = 0; // cout << "===="; for(int i = 0; i*l+k <= n; i++){ ans += comb[n][i*l+k]*mint(m).pow(i); // cout << comb[n][i*l+k]*mint(m).pow(i) << ' '; } // cout << endl; return ans; } void test(){ for(int n = 1; n <= 10; n++){ for(int m = 1; m <= 10; m++){ for(int l = 1; l <= 10; l++){ for(int k = 0; k < l; k++){ for(int b = 1; b <= 10; b++){ mint a0 = solve(n, m, l, k, b); mint a1 = naive(n, m, l, k, b); if(a0 != a1){ cout << n << ' ' << m << ' ' << l << ' ' << k << ' ' << b << ':'; cout << a0 << ' ' << a1 << endl; } } } } } } cout << "OK" << endl; } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; // test(); ll n, m; int l, k, b; cin >> n >> m >> l >> k >> b; cout << solve(n, m, l, k, b) << endl; // cout << naive(n, m, l, k, b) << endl; }