#include <bits/stdc++.h>
using namespace std;
const int N = 1100000;
int a[N], b[N], c[N], f[N];
unsigned long long p[100];
int n, m;
long long T;
int mod, phi, cnt;
int mod1, mod2;
long long k1, k2;
int ans;
struct FWT1 {
  int a[N], b[N];
  int power(int x, long long y) {
    int ret = 1;
    for (; y; y >>= 1, x = 1ll * x * x % mod) {
      if (y & 1) ret = 1ll * ret * x % mod;
    }
    return ret;
  }
  void FWT(int a[]) {
    int i, j, k, x, y;
    for (i = 1; i < n; i <<= 1) {
      for (j = 0; j < n; j += (i << 1)) {
        for (k = 0; k < i; k++) {
          x = a[j + k];
          y = a[j + k + i];
          a[j + k] = (x + y) % mod;
          a[j + k + i] = (x - y) % mod;
        }
      }
    }
  }
  void work() {
    int i, INV;
    FWT(a);
    FWT(b);
    for (i = 0; i <= n - 1; i++) a[i] = power(a[i], T);
    for (i = 0; i <= n - 1; i++) a[i] = 1ll * a[i] * b[i] % mod;
    FWT(a);
    INV = power(power(2, m), phi - 1);
    for (i = 0; i <= n - 1; i++) a[i] = 1ll * a[i] * INV % mod;
    for (i = 0; i <= n - 1; i++) a[i] = a[i] < 0 ? a[i] + mod : a[i];
  }
};
FWT1 F1;
void init() {
  int i;
  p[0] = 1;
  for (i = 1; i <= 62; i++) p[i] = p[i - 1] * 2;
}
struct FWT2 {
  unsigned long long power(unsigned long long x, long long y) {
    unsigned long long ret = 1;
    for (; y; y >>= 1, x = x * x) {
      if (y & 1) ret = ret * x;
    }
    return ret;
  }
  unsigned long long a[N], b[N];
  void FWT(unsigned long long a[]) {
    int i, j, k;
    unsigned long long x, y;
    for (i = 1; i < n; i <<= 1) {
      for (j = 0; j < n; j += (i << 1)) {
        for (k = 0; k < i; k++) {
          x = a[j + k];
          y = a[j + k + i];
          a[j + k] = x + y;
          a[j + k + i] = x - y;
        }
      }
    }
  }
  void work() {
    int i, j;
    unsigned long long x;
    long long now;
    FWT(a);
    FWT(b);
    for (i = 0; i <= n - 1; i++) a[i] = power(a[i], T);
    for (i = 0; i <= n - 1; i++) a[i] *= b[i];
    FWT(a);
    for (i = 0; i <= n - 1; i++) a[i] /= p[m];
    for (i = 0; i <= n - 1; i++) a[i] &= (1 << cnt) - 1;
  }
};
FWT2 F2;
void getphi() {
  int x = mod;
  phi = mod;
  int i;
  for (i = 2; i * i <= mod; i++) {
    if (x % i == 0) phi = phi / i * (i - 1);
    while (x % i == 0) x /= i;
  }
  if (x > 1) phi = phi / x * (x - 1);
}
void exgcd(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return;
  }
  exgcd(b, a % b, y, x);
  y -= a / b * x;
}
int main() {
  int i;
  int r1, r2;
  init();
  scanf("%d%I64d%d", &m, &T, &mod);
  n = (1 << m);
  while (mod % 2 == 0) {
    cnt++;
    mod >>= 1;
  }
  getphi();
  for (i = 0; i <= n - 1; i++) scanf("%d", &b[i]);
  for (i = 0; i <= m; i++) scanf("%d", &c[i]);
  for (i = 1; i <= n - 1; i++) f[i] = f[i >> 1] + (i & 1);
  for (i = 0; i <= n - 1; i++) a[i] = c[f[i]];
  for (i = 0; i <= n - 1; i++) F1.a[i] = a[i], F1.b[i] = b[i];
  for (i = 0; i <= n - 1; i++) F2.a[i] = a[i], F2.b[i] = b[i];
  F1.work();
  F2.work();
  mod1 = mod;
  mod2 = (1 << cnt);
  exgcd(mod1, mod2, k1, k2);
  for (i = 0; i <= n - 1; i++) {
    r1 = F1.a[i];
    r2 = F2.a[i];
    ans = (1ll * mod1 * (r2 - r1) % (mod1 * mod2) * k1 + r1) % (mod1 * mod2);
    ans = (ans + mod1 * mod2) % (mod1 * mod2);
    printf("%d\n", ans);
  }
}

### Prompt

Create a solution in cpp for the following problem:

The Elements of Harmony are six supernatural artifacts representing subjective aspects of harmony. They are arguably the most powerful force in Equestria. The inside of Elements of Harmony can be seen as a complete graph with n vertices labeled from 0 to n - 1, where n is a power of two, equal to 2m.

<image>

The energy in Elements of Harmony is in constant movement. According to the ancient book, the energy of vertex u in time i (ei[u]) equals to: 

<image>

Here b[] is the transformation coefficient — an array of m + 1 integers and f(u, v) is the number of ones in the binary representation of number (u xor v).

Given the transformation coefficient and the energy distribution at time 0 (e0[]). Help Twilight Sparkle predict the energy distribution at time t (et[]). The answer can be quite large, so output it modulo p.

Input

The first line contains three integers m, t and p (1 ≤ m ≤ 20; 0 ≤ t ≤ 1018; 2 ≤ p ≤ 109). The following line contains n (n = 2m) integers e0[i] (1 ≤ e0[i] ≤ 109; 0 ≤ i < n). The next line contains m + 1 integers b[i] (0 ≤ b[i] ≤ 109; 0 ≤ i ≤ m).

Output

Output n lines, the i-th line must contain a single integer et[i] modulo p.

Examples

Input

2 2 10000
4 1 2 3
0 1 0


Output

14
6
6
14

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 1100000;
int a[N], b[N], c[N], f[N];
unsigned long long p[100];
int n, m;
long long T;
int mod, phi, cnt;
int mod1, mod2;
long long k1, k2;
int ans;
struct FWT1 {
  int a[N], b[N];
  int power(int x, long long y) {
    int ret = 1;
    for (; y; y >>= 1, x = 1ll * x * x % mod) {
      if (y & 1) ret = 1ll * ret * x % mod;
    }
    return ret;
  }
  void FWT(int a[]) {
    int i, j, k, x, y;
    for (i = 1; i < n; i <<= 1) {
      for (j = 0; j < n; j += (i << 1)) {
        for (k = 0; k < i; k++) {
          x = a[j + k];
          y = a[j + k + i];
          a[j + k] = (x + y) % mod;
          a[j + k + i] = (x - y) % mod;
        }
      }
    }
  }
  void work() {
    int i, INV;
    FWT(a);
    FWT(b);
    for (i = 0; i <= n - 1; i++) a[i] = power(a[i], T);
    for (i = 0; i <= n - 1; i++) a[i] = 1ll * a[i] * b[i] % mod;
    FWT(a);
    INV = power(power(2, m), phi - 1);
    for (i = 0; i <= n - 1; i++) a[i] = 1ll * a[i] * INV % mod;
    for (i = 0; i <= n - 1; i++) a[i] = a[i] < 0 ? a[i] + mod : a[i];
  }
};
FWT1 F1;
void init() {
  int i;
  p[0] = 1;
  for (i = 1; i <= 62; i++) p[i] = p[i - 1] * 2;
}
struct FWT2 {
  unsigned long long power(unsigned long long x, long long y) {
    unsigned long long ret = 1;
    for (; y; y >>= 1, x = x * x) {
      if (y & 1) ret = ret * x;
    }
    return ret;
  }
  unsigned long long a[N], b[N];
  void FWT(unsigned long long a[]) {
    int i, j, k;
    unsigned long long x, y;
    for (i = 1; i < n; i <<= 1) {
      for (j = 0; j < n; j += (i << 1)) {
        for (k = 0; k < i; k++) {
          x = a[j + k];
          y = a[j + k + i];
          a[j + k] = x + y;
          a[j + k + i] = x - y;
        }
      }
    }
  }
  void work() {
    int i, j;
    unsigned long long x;
    long long now;
    FWT(a);
    FWT(b);
    for (i = 0; i <= n - 1; i++) a[i] = power(a[i], T);
    for (i = 0; i <= n - 1; i++) a[i] *= b[i];
    FWT(a);
    for (i = 0; i <= n - 1; i++) a[i] /= p[m];
    for (i = 0; i <= n - 1; i++) a[i] &= (1 << cnt) - 1;
  }
};
FWT2 F2;
void getphi() {
  int x = mod;
  phi = mod;
  int i;
  for (i = 2; i * i <= mod; i++) {
    if (x % i == 0) phi = phi / i * (i - 1);
    while (x % i == 0) x /= i;
  }
  if (x > 1) phi = phi / x * (x - 1);
}
void exgcd(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return;
  }
  exgcd(b, a % b, y, x);
  y -= a / b * x;
}
int main() {
  int i;
  int r1, r2;
  init();
  scanf("%d%I64d%d", &m, &T, &mod);
  n = (1 << m);
  while (mod % 2 == 0) {
    cnt++;
    mod >>= 1;
  }
  getphi();
  for (i = 0; i <= n - 1; i++) scanf("%d", &b[i]);
  for (i = 0; i <= m; i++) scanf("%d", &c[i]);
  for (i = 1; i <= n - 1; i++) f[i] = f[i >> 1] + (i & 1);
  for (i = 0; i <= n - 1; i++) a[i] = c[f[i]];
  for (i = 0; i <= n - 1; i++) F1.a[i] = a[i], F1.b[i] = b[i];
  for (i = 0; i <= n - 1; i++) F2.a[i] = a[i], F2.b[i] = b[i];
  F1.work();
  F2.work();
  mod1 = mod;
  mod2 = (1 << cnt);
  exgcd(mod1, mod2, k1, k2);
  for (i = 0; i <= n - 1; i++) {
    r1 = F1.a[i];
    r2 = F2.a[i];
    ans = (1ll * mod1 * (r2 - r1) % (mod1 * mod2) * k1 + r1) % (mod1 * mod2);
    ans = (ans + mod1 * mod2) % (mod1 * mod2);
    printf("%d\n", ans);
  }
}

```