易知:
[A(n-1), A] * [ A, 0 = [A(n), A]
1, 1]
可以用快速幂加速
(如果不是练习矩阵加速有更好的做法 这里不给出)
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
using namespace std;
#define MAXN 30
#define MAXM 30
typedef int LL;
struct Maxtrix{
int n, m;
LL A[MAXN+10][MAXN+10];
};
LL a[MAXN+10], f[MAXN+10];
int n, k;
LL p;
Maxtrix A, B, E;
Maxtrix ST[1][2], M[2][2], C[2][2];
void init(Maxtrix &X)
{
X.n = X.m = 0;
memset(X.A, 0, sizeof(X.A));
}
void Get_E()
{
E.n = E.m = MAXN;
for(int i = 0; i < E.n; i++)
E.A[i][i] = 1;
}
Maxtrix add(Maxtrix AA, Maxtrix BB)
{
Maxtrix D; D = AA;
for(int i = 0; i < AA.n; i++)
for(int j = 0; j < AA.m; j++)
{
D.A[i][j] += BB.A[i][j];
D.A[i][j] %= p;
}
return D;
}
Maxtrix mul(Maxtrix AA, Maxtrix BB)
{
Maxtrix D;
init(D);
D.n = AA.n;
D.m = BB.m;
for(int i = 0; i < AA.n; i++)
for(int j = 0; j < BB.n; j++)
for(int k = 0; k < BB.m; k++)
{
D.A[i][k] += (AA.A[i][j] * BB.A[j][k]) % p;
D.A[i][k] %= p;
}
return D;
}
Maxtrix pow_mod(Maxtrix &A, int k)
{
Maxtrix ans = E, t = A;
ans.n = A.n;
ans.m = A.m;
while(k)
{
if(k & 1)
ans = mul(ans, t);
t = mul(t, t);
k >>= 1;
}
return ans;
}
void dou_mul(Maxtrix A[][2], Maxtrix BB[][2], Maxtrix C[][2])
{
Maxtrix D[2][2];
for(int i = 0; i < 2; i++)
for(int j = 0; j < 2; j++)
D[i][j] = B;
for(int i = 0; i < 2; i++)
for(int j = 0; j < 2; j++)
for(int k = 0; k < 2; k++)
{
Maxtrix tmp;
tmp = mul(A[i][j], BB[j][k]);
D[i][k] = add(D[i][k], tmp);
}
memcpy(C, D, sizeof(D));
}
void dou_pow_mod(int k, Maxtrix Ans[][2])
{
Maxtrix ans[2][2], t[2][2];
for(int i = 0; i < 2; i++) { ans[i][i] = E; ans[i][i ^ 1] = B; }
memcpy(t, M, sizeof(M));
while(k)
{
if(k & 1) dou_mul(ans, t, ans);
dou_mul(t, t, t);
k >>= 1;
}
memcpy(Ans, ans, sizeof(ans));
}
int main()
{
Get_E();
while(cin >> n >> k >> p && n+k+p)
{
init(A);
init(B); B.n = B.m = n;
E.n = E.m = A.n = A.m = n;
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
cin >> A.A[i][j];
ST[0][0] = ST[0][1] = A;
M[0][0] = A; M[0][1] = B; M[1][0] = E; M[1][1] = E;
Maxtrix tmp[2][2];
dou_pow_mod(k-1, tmp);
dou_mul(ST, tmp, tmp);
Maxtrix ANS = tmp[0][0];
for(int i = 0; i < n; i++)
{
printf("%d", ANS.A[i][0]);
for(int j = 1; j < n; j++)
printf(" %d", ANS.A[i][j]);
puts(" ");
}
}
}