problem Description Lele now is thinking about a simple function f(x).
If x < 10 f(x) = x. If x >= 10 f(x) = a0 * f(x-1) + a1 * f(x-2) + a2 * f(x-3) + …… + a9 * f(x-10); And ai(0<=i<=9) can only be 0 or 1 .
Now, I will give a0 ~ a9 and two positive integers k and m ,and could you help Lele to caculate f(k)%m.
Input The problem contains mutiple test cases.Please process to the end of file. In each case, there will be two lines. In the first line , there are two positive integers k and m. ( k<2*10^9 , m < 10^5 ) In the second line , there are ten integers represent a0 ~ a9.
Output For each case, output f(k) % m in one line.
Sample Input
10 9999 1 1 1 1 1 1 1 1 1 1 20 500 1 0 1 0 1 0 1 0 1 0
Sample Output
45 104
Author linle
Source 2007省赛集训队练习赛（6）_linle专场
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很明显的矩阵递推题
/*************************************************************************> File Name: hdu1757.cpp> Author: ALex> Mail: zchao1995@gmail.com> Created Time: 2015年03月11日 星期三 19时57分20秒 ************************************************************************/;const double pi = acos(-1);const int inf = 0x3f3f3f3f;const double eps = 1e-15;LL;typedef pair <int, int> PLL;int mod;class MARTIX{public:int mat[105][105];MARTIX();MARTIX operator + (const MARTIX &b)const;MARTIX operator * (const MARTIX &b)const;MARTIX & operator = (const MARTIX &b);};MARTIX :: MARTIX(){memset (mat, 0, sizeof(mat));}MARTIX MARTIX :: operator + (const MARTIX &b)const{MARTIX ret;for (int i = 0; i < 10; ++i){for (int j = 0; j < 10; ++j){ret.mat[i][j] = mat[i][j] + b.mat[i][j];ret.mat[i][j] %= mod;}}return ret;}MARTIX MARTIX :: operator * (const MARTIX &b)const{MARTIX ret;for (int i = 0; i < 10; ++i){for (int j = 0; j < 10; ++j){ret.mat[i][j] = 0;for (int k = 0; k < 10; ++k){ret.mat[i][j] += mat[i][k] * b.mat[k][j];ret.mat[i][j] %= mod;}}}return ret;}MARTIX & MARTIX :: operator = (const MARTIX &b){for (int i = 0; i < 10; ++i){for (int j = 0; j < 10; ++j){this -> mat[i][j] = b.mat[i][j];}}return *this;}MARTIX fastpow(MARTIX A, LL n){MARTIX ans;for (int i = 0; i < 10; ++i){for (int j = 0; j < 10; ++j){ans.mat[i][j] = (i == j);}}while (n){if (n & 1){ans = ans * A;}n >>= 1;A = A * A;}return ans;}void Debug(MARTIX A){for (int i = 0; i < 10; ++i){for (int j = 0; j < 10; ++j){printf(“%d “, A.mat[i][j]);}printf(“\n”);}}int main (){LL k;while (~scanf(“%lld%d”, &k, &mod)){if (k < 10){printf(“%lld\n”, k);continue;}MARTIX A;for (int i = 0; i < 10; ++i){scanf(“%d”, &A.mat[i][0]);}for (int i = 0; i < 9; ++i){A.mat[i][i + 1] = 1;}MARTIX ans = fastpow(A, k – 9);MARTIX F;for (int i = 0; i < 10; ++i){F.mat[0][i] = 10 – i – 1;}//Debug(F);ans = F * ans;printf(“%d\n”, ans.mat[0][0]);}return 0;}
，没有行李，没有背包，不带电脑更不要手机，
