#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
map<int, int> mp, mp2;
int a, b, mod, top, q[500000 + 5], step[500000 + 5];
inline int pow(int x, int k) {
  int res = 1;
  for (; k; k >>= 1, x = 1LL * x * x % mod)
    if (k & 1) res = 1LL * res * x % mod;
  return res;
}
void Add(int x, int way, int s) {
  if (mp[x]) return;
  mp[x] = way;
  if (top < 500000) q[++top] = x, step[top] = s;
}
int Ans[105], Ans2[105], ans, ans2;
void Try(int x, int way, int s) {
  if (mp2[x]) return;
  mp2[x] = way;
  if (mp[x]) {
    for (int i = x; i != a;) {
      Ans[++ans] = mp[i];
      if (Ans[ans] == 3)
        i = pow(i, mod - 2);
      else
        i = (i + (Ans[ans] < 2 ? mod - 1 : 1)) % mod;
    }
    for (int i = x; i != b;) {
      Ans2[++ans2] = mp2[i];
      if (Ans2[ans2] == 3)
        i = pow(i, mod - 2);
      else
        Ans2[ans2] ^= 3, i = (i + (Ans2[ans2] < 2 ? 1 : mod - 1)) % mod;
    }
    printf("%d\n", ans + ans2);
    for (int j = ans; j; --j) printf("%d ", Ans[j]);
    for (int j = 1; j <= ans2; ++j) printf("%d ", Ans2[j]);
    exit(0);
  }
  if (top < 500000) q[++top] = x, step[top] = s;
}
int main() {
  a = read();
  b = read();
  mod = read();
  Add(a, 0, 0);
  for (int i = 1; i <= top; ++i) {
    int x = q[i];
    if (step[i] >= 100) continue;
    Add((x + 1) % mod, 1, step[i] + 1);
    Add((x + mod - 1) % mod, 2, step[i] + 1);
    Add(pow(x, mod - 2), 3, step[i] + 1);
  }
  top = 0;
  Try(b, 0, 0);
  for (int i = 1; i <= top; ++i) {
    int x = q[i];
    if (step[i] >= 100) continue;
    Try((x + 1) % mod, 1, step[i] + 1);
    Try((x + mod - 1) % mod, 2, step[i] + 1);
    Try(pow(x, mod - 2), 3, step[i] + 1);
  }
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

Allen is playing Number Clicker on his phone.

He starts with an integer u on the screen. Every second, he can press one of 3 buttons.

  1. Turn u → u+1 \pmod{p}. 
  2. Turn u → u+p-1 \pmod{p}. 
  3. Turn u → u^{p-2} \pmod{p}. 



Allen wants to press at most 200 buttons and end up with v on the screen. Help him!

Input

The first line of the input contains 3 positive integers: u, v, p (0 ≤ u, v ≤ p-1, 3 ≤ p ≤ 10^9 + 9). p is guaranteed to be prime.

Output

On the first line, print a single integer ℓ, the number of button presses. On the second line, print integers c_1, ..., c_ℓ, the button presses. For 1 ≤ i ≤ ℓ, 1 ≤ c_i ≤ 3.

We can show that the answer always exists.

Examples

Input

1 3 5


Output

2
1 1


Input

3 2 5


Output

1
3

Note

In the first example the integer on the screen changes as 1 → 2 → 3.

In the second example the integer on the screen changes as 3 → 2. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
map<int, int> mp, mp2;
int a, b, mod, top, q[500000 + 5], step[500000 + 5];
inline int pow(int x, int k) {
  int res = 1;
  for (; k; k >>= 1, x = 1LL * x * x % mod)
    if (k & 1) res = 1LL * res * x % mod;
  return res;
}
void Add(int x, int way, int s) {
  if (mp[x]) return;
  mp[x] = way;
  if (top < 500000) q[++top] = x, step[top] = s;
}
int Ans[105], Ans2[105], ans, ans2;
void Try(int x, int way, int s) {
  if (mp2[x]) return;
  mp2[x] = way;
  if (mp[x]) {
    for (int i = x; i != a;) {
      Ans[++ans] = mp[i];
      if (Ans[ans] == 3)
        i = pow(i, mod - 2);
      else
        i = (i + (Ans[ans] < 2 ? mod - 1 : 1)) % mod;
    }
    for (int i = x; i != b;) {
      Ans2[++ans2] = mp2[i];
      if (Ans2[ans2] == 3)
        i = pow(i, mod - 2);
      else
        Ans2[ans2] ^= 3, i = (i + (Ans2[ans2] < 2 ? 1 : mod - 1)) % mod;
    }
    printf("%d\n", ans + ans2);
    for (int j = ans; j; --j) printf("%d ", Ans[j]);
    for (int j = 1; j <= ans2; ++j) printf("%d ", Ans2[j]);
    exit(0);
  }
  if (top < 500000) q[++top] = x, step[top] = s;
}
int main() {
  a = read();
  b = read();
  mod = read();
  Add(a, 0, 0);
  for (int i = 1; i <= top; ++i) {
    int x = q[i];
    if (step[i] >= 100) continue;
    Add((x + 1) % mod, 1, step[i] + 1);
    Add((x + mod - 1) % mod, 2, step[i] + 1);
    Add(pow(x, mod - 2), 3, step[i] + 1);
  }
  top = 0;
  Try(b, 0, 0);
  for (int i = 1; i <= top; ++i) {
    int x = q[i];
    if (step[i] >= 100) continue;
    Try((x + 1) % mod, 1, step[i] + 1);
    Try((x + mod - 1) % mod, 2, step[i] + 1);
    Try(pow(x, mod - 2), 3, step[i] + 1);
  }
  return 0;
}

```