#include using namespace std; using ll = long long; using pii = pair; template using V = vector; template using VV = V>; #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i, n) rep2(i, 0, n) #define rep2(i, m, n) for (int i = m; i < (n); i++) #define per(i, b) per2(i, 0, b) #define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--) #define ALL(c) (c).begin(), (c).end() #define SZ(x) ((int)(x).size()) constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template void chmin(T& t, const U& u) { if (t > u) t = u; } template void chmax(T& t, const U& u) { if (t < u) t = u; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } template ostream& operator<<(ostream& os, const vector& v) { os << "{"; rep(i, v.size()) { if (i) os << ","; os << v[i]; } os << "}"; return os; } #ifdef LOCAL void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif template struct ModInt { using uint = unsigned int; using ull = unsigned long long; using M = ModInt; uint v; ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); } M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD) v = (_v < MOD) ? _v : _v - MOD; return *this; } explicit operator bool() const { return v != 0; } M operator+(const M& a) const { return M().set_norm(v + a.v); } M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); } M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); } M operator/(const M& a) const { return *this * a.inv(); } M& operator+=(const M& a) { return *this = *this + a; } M& operator-=(const M& a) { return *this = *this - a; } M& operator*=(const M& a) { return *this = *this * a; } M& operator/=(const M& a) { return *this = *this / a; } M operator-() const { return M() - *this; } M& operator++(int) { return *this = *this + 1; } M& operator--(int) { return *this = *this - 1; } M pow(ll n) const { if (n < 0) return inv().pow(-n); M x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } M inv() const { ll a = v, b = MOD, p = 1, q = 0, t; while (b != 0) { t = a / b; swap(a -= t * b, b); swap(p -= t * q, q); } return M(p); } bool operator==(const M& a) const { return v == a.v; } bool operator!=(const M& a) const { return v != a.v; } friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; } static uint get_mod() { return MOD; } }; using Mint = ModInt<1000000007>; int pr_root(int p) { for (int i = 1; i < p; ++i) { set st; int x = 1; bool ok = 1; rep(t, p - 1) { if (st.count(x)) { ok = 0; break; } st.insert(x); x = x * i % p; } if (ok) { return i; } } } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int p, n, k, b; cin >> p >> n >> k >> b; V a(n); rep(i, n) cin >> a[i]; k = __gcd(k, p - 1); int g = pr_root(p); // dp[i][j] : ..i, mod p = r^j, j = k : 0 VV dp(n + 1, V(k + 1)); dp[0][k] = 1; V rk(p), pw(p); { int x = 1; rep(t, p - 1) { pw[t] = x; rk[x] = t; x = x * g % p; } } debug(k, rk); rep(i, n) { rep(j, k + 1) { // x=0 dp[i + 1][j] += dp[i][j]; int v = j == k ? 0 : pw[j]; for (int x = 0; x < (p - 1) / k; ++x) { int nv = (v + ll(pw[x * k]) * a[i]) % p; if (nv == 0) { dp[i + 1][k] += dp[i][j] * k; } else { dp[i + 1][rk[nv] % k] += dp[i][j] * k; } } } } int c = b == 0 ? k : rk[b] % k; int cnt = 0; for (int i = 1; i < p; ++i) { if (rk[i] % k == c) cnt++; } debug(dp[n]); if (b > 0) { if (cnt > 0) { cout << dp[n][c] / cnt << endl; } else { cout << 0 << endl; } } else { cout << dp[n][k] << endl; } return 0; }