
```cpp
#include <bits/stdc++.h>
using namespace std;
vector<int> mul(vector<int> &A, vector<int> &B) { 
    int i, j;
    vector<int> C(A.size() + B.size());
    for (i = 0; i < A.size(); i++) {
        for (j = 0; j < B.size(); j++) {
            C[i + j] += A[i] * B[j];
        }
    }
    int temp = 0;
    for (i = 0; i < C.size(); i++) {
        temp += C[i];
        C[i] = temp % 10;
        temp /= 10;
    }
    while (C.size() < 500) C.push_back(0); 
    if (C.size() > 500) {	
        C.resize(500);	
    }
    return C;
}
vector<int> poww(int b) {
    vector<int> A, B;
    string a = "1";
    string base = "2";
    int i;
    for (i = a.size() - 1; i >= 0; i--) A.push_back(a[i] - '0');
    for (i = base.size() - 1; i >= 0; i--) B.push_back(base[i] - '0');
    while (b != 0) {       
        if (b & 1 != 0) A = mul(A, B);
        B = mul(B, B);
        b >>= 1;
    }
    return A;
}

int main() {
    vector<int> C;
    int P, N, i;
    cin >> P;
    N = P * log10(2) + 1;
    cout << N << endl;
    C = poww(P);
    C[0]--;
    for (i = C.size() - 1; i >= 0; i--) {
        cout << C[i];
    }
    return 0;
}
```
太经典的快速幂了
