参考这篇题解写的

#include <bits/stdc++.h>
#define int long long
#define int1 __int128
#define uint unsigned long long
#define lowbit(x) (x & -x)
using namespace std;

namespace fastio
{
    const int bufl = 1 << 20;
    struct IN
    {
        FILE *IT = stdin;
        char ibuf[bufl], *is = ibuf, *it = ibuf;
        inline char getChar()
        {
            if (is == it)
            {
                it = (is = ibuf) + fread(ibuf, 1, bufl, IT);
                if (is == it)
                    return EOF;
            }
            return *is++;
        }
        IN &operator>>(int &a)
        {
            a = 0;
            int b = 0, c = getChar();
            while (c < 48 || c > 57)
                b ^= (c == 45), c = getChar();
            while (c >= 48 && c <= 57)
                a = (a << 1) + (a << 3) + c - 48, c = getChar();
            if (b)
                a = -a;
            return *this;
        }
    } fin;
}
// #define cin fastio::fin

const int DM[8][2] = {0, 1, 1, 0, 0, -1, -1, 0, 1, 1, 1, -1, -1, 1, -1, -1};
const int HM = 5644863343;
const int HB = 131;
const int HI = 1e5 + 3;
const int N = 100001;
void write(int1 x)
{
    if (x > 9)
        write(x / 10);
    putchar(x % 10 | 48);
}
void exgcd(int a, int b, int1 &x, int1 &y)
{
    if (!b)
    {
        x = 1;
        y = 0;
        return;
    }
    exgcd(b, a % b, x, y);
    int1 t = x;
    x = y;
    y = t - (a / b) * y;
    return;
}
int1 inv(int a, int p)
{
    int1 x, y;
    exgcd(a, p, x, y);
    x %= p;
    if (x < 0)
    {
        x += p;
    }
    return x;
}
int1 qpow(int x, int k)
{
    if (k == 0)
    {
        return 1;
    }
    int1 tmp = qpow(x, k >> 1);
    tmp *= tmp;
    if (k & 1)
    {
        return x * tmp;
    }
    return tmp;
}
int1 niu(int a, int p)
{
    a /= p;
    int1 res = a;
    while (a)
    {
        a /= p;
        res += a;
    }
    return res;
}
int1 wilson(int a, int p, int pc)
{
    int1 ans = 1;
    vector<int1> f(pc + 5);
    f[0] = 1;
    for (int i = 1; i < pc; i++)
    {
        if (i % p)
        {
            f[i] = f[i - 1] * i % pc;
        }
        else
        {
            f[i] = f[i - 1];
        }
    }
    bool fl = (p != 2 || pc <= 4);
    while (a > 1)
    {
        if (fl & (a / pc))
        {
            ans = pc - ans;
        }
        ans = ans * f[a % pc] % pc;
        a /= p;
    }
    return ans;
}
int1 crt(vector<int1> a, vector<int1> p)
{
    int1 ans = 0, prd = 1;
    for (auto v : p)
    {
        prd *= v;
    }
    for (int i = 0; i < a.size(); i++)
    {
        int1 k = prd / p[i], x, y;
        // write(k);
        // cout<<' ';
        // write(a[i]);
        // cout<<'\n';
        exgcd(k, p[i], x, y);
        ans = (ans + k * a[i] * x % prd) % prd;
    }
    return (ans % prd + prd) % prd;
}
int1 exlucas(int n, int m, int1 MOD)
{
    vector<int1> p, pc;
    int1 tp = MOD;
    for (int i = 2; i * i <= tp; i++)
    {
        if (tp % i == 0)
        {
            p.push_back(i);
            int res = 1;
            while (tp % i == 0)
            {
                res *= i;
                tp /= i;
            }
            pc.push_back(res);
        }
    }
    if (tp)
    {
        p.push_back(tp);
        pc.push_back(tp);
    }
    vector<int1> a;
    // cout << "check\n";
    for (int i = 0; i < p.size(); i++)
    {
        int1 nw = wilson(n, p[i], pc[i]), mw = wilson(m, p[i], pc[i]), nmw = wilson(n - m, p[i], pc[i]);
        a.push_back(nw * inv(mw * nmw % pc[i], pc[i]) * qpow(pc[i], niu(n, p[i]) - niu(m, p[i]) - niu(n - m, p[i])));
    }
    return crt(a, pc);
}
inline int read()
{
    char c = getchar();
    int x = 0, s = 1;
    while (c < '0' || c > '9')
    {
        if (c == '-')
            s = -1;
        c = getchar();
    }
    while (c >= '0' && c <= '9')
    {
        x = x * 10 + c - '0';
        c = getchar();
    }
    return x * s;
}
signed main()
{
    int1 n, m, p;
    n = read();
    m = read();
    p = read();
    write(exlucas(n, m, p));
    // cout << '\n';
    // write(wilson(5, 3, 3));
    // cout << ;
}