1 #include<cmath>
 2 #include<cstdio>
 3 #include<cstdlib>
 4 #include<cstring>
 5 #include<iostream>
 6 #include<algorithm>
 7 using namespace std;
 8 typedef long long lo;
 9 inline int Get()
10 {
11     int x;
12     char c;
13     bool o = false;
14     while((c = getchar()) < '0' || c > '9')
15         if(c == '-') o = true;
16     x = c - '0';
17     while((c = getchar()) >= '0' && c <= '9')
18         x = x * 10 + c - '0';
19     return (o) ? -x : x;
20 }
21 const int maxn = 2333;
22 int f[maxn][maxn];
23 int fac[maxn];
24 int x[maxn], y[maxn];
25 int a, n, m, mo;
26 int z, v, ans;
27 int num;
28 inline void Dp()
29 {
30     f[0][0] = 1;
31     for(int i = 1; i <= m; ++i)
32         for(int j = 0; j <= n; ++j)
33         {
34             f[i][j] = f[i - 1][j];
35             if(j) f[i][j] += (lo) f[i - 1][j - 1] * i % mo;
36             if(f[i][j] >= mo) f[i][j] -= mo;
37         }
38 }
39 inline void Fac()
40 {
41     fac[0] = 1;
42     for(int i = 1; i <= n; ++i) fac[i] = (lo) fac[i - 1] * i % mo;
43 }
44 inline void Sun()
45 {
46     num = 0;
47     for(int i = 0; i <= m; ++i)
48         if(f[i][n])
49         {
50             x[++num] = i, y[num] = f[i][n];
51             if(num == (n << 1 | 1)) return;
52         }
53 }
54 inline int Mod(int x)
55 {
56     if(x < 0) x += mo;
57     return x;
58 }
59 inline int Pow(int x, int n)
60 {
61     int sum = 1;
62     while(n)
63     {
64         if(n & 1) sum = (lo) sum * x % mo;
65         x = (lo) x * x % mo;
66         n >>= 1;
67     }
68     return sum;
69 }
70 int main()
71 {
72     a = Get(), n = Get(), mo = Get();
73     m = n << 2;
74     Dp();
75     Fac();
76     if(m >= a)
77     {
78         printf("%d", (lo) f[a][n] * fac[n] % mo);
79         return 0;
80     }
81     Sun();
82     z = 1;
83     for(int i = 1; i <= num; ++i) z = (lo) z * Mod(a - x[i]) % mo;
84     for(int i = 1; i <= num; ++i)
85     {
86         v = Mod(a - x[i]);
87         for(int j = 1; j <= num; ++j)
88             if(i != j)
89                 v = (lo) v * Mod(x[i] - x[j]) % mo;
90         ans = ans + (lo) y[i] * z % mo * Pow(v, mo - 2) % mo;
91         if(ans >= mo) ans -= mo;
92     }
93     printf("%d", (lo) ans * fac[n] % mo);
94 }