51Nod-1436 方程的解数

题目链接 

题解链接

版权属于以上链接

#include <iostream>

#define mod(a, m) ((a) % (m) + (m)) % (m)

using namespace std;

typedef long long ll;

const int MAGIC = ;

ll n, k, l, m;

struct matrix
{
    ll c[][];
} a;

ll f[];

void ans_cf(matrix a)
{
    f[] = mod(a.c[][] + a.c[][], m);
    f[] = mod(a.c[][] + a.c[][], m);
}

matrix matrix_cf(matrix a, matrix b)
{
    matrix ans;
    for (int i = ; i < ; i++)
    {
        for (int j = ; j < ; j++)
        {
            ans.c[i][j] = ;
            for (int k = ; k < ; k++)
            {
                ans.c[i][j] += a.c[k][i] * b.c[j][k];
                ans.c[i][j] = mod(ans.c[i][j], m);
            }
        }
    }

    return ans;
}

matrix matrix_pow(matrix a, ll n)
{
    matrix ans;
    ans.c[][] = ans.c[][] = ;
    ans.c[][] = ans.c[][] = ;
    while (n)
    {
        if (n & )
        {
            ans = matrix_cf(ans, a);
        }
        n = n >> ;
        a = matrix_cf(a, a);
    }

    return ans;
}

ll qpow(ll a, ll b)
{
    ll ans = ;
    while (b)
    {
        if (b & )
        {
            ans = mod(ans * a, m);
        }
        b = b >> ;
        a = mod(a * a, m);
    }

    return ans;
}

void init()
{
    a.c[][] = a.c[][] = a.c[][] = ;
    a.c[][] = ;
}

int main(int argc, const char * argv[])
{
    cin >> n >> k >> l >> m;

    unsigned long long t = 1ULL << l;
    if (m ==  || (k >= t && l != MAGIC))
    {
        cout <<  << '\n';
        return ;
    }

    init();
    a = matrix_pow(a, n);
    ans_cf(a);
    ll x = f[], y = mod(qpow(, n) - x, m);

    int cnt_0 = , cnt_1 = ;
    while (k)
    {
        if (k % )
        {
            cnt_1++;
        }
        else
        {
            cnt_0++;
        }
        k >>= ;
    }
    cnt_0 += l - cnt_0 - cnt_1;

    ll ans = mod(mod(qpow(x, cnt_0), m) * mod(qpow(y, cnt_1), m), m);
    cout << ans << '\n';

    return ;
}