// matrix power in A^p in O(log(p))
vector<vector<int>> matrix_pow(const vector<vector<int>>& A, int p)
{
if (p == 1)
return A;
if (p % 2 == 1)
return matrix_mul(A, matrix_pow(A, p - 1));
auto B = matrix_pow(A, p / 2);
return matrix_mul(B, B);
}
int main()
{
matrix_t m1, m2;
std::scanf("%s %s %d %d %d %d", n, m, &a, &b, &c, &d);
m1.m[0][0] = a % mod_v, m1.m[0][1] = b % mod_v;
m2.m[0][0] = c % mod_v, m2.m[0][1] = d % mod_v;
dec(n), dec(m);
m1 = matrix_pow(m1, m);
m2 = m1 * matrix_pow(m2 * m1, n);
std::printf("%lld\n", (m2.m[0][0] + m2.m[0][1]) % mod_v);
return 0;
}
matrix_t matrix_pow(matrix_t x, const char* p)
{
matrix_t ans;
int len = std::strlen(p);
int start = 0;
while(p[start] == '0') ++start;
for(int i = len - 1; i >= start; --i)
{
ans = matrix_pow(x, p[i] - '0') * ans;
x = matrix_pow(x, 10);
}
return ans;
}
// Matrix Exponentiation - O(log(n))
int matrix_fibo(int n)
{
if (n == 0)
return 0;
if (n == 1)
return 1;
vector<vector<int>> M = { { 1, 1 }, { 1, 0 } };
auto res = matrix_pow(M, n - 1);
return res[0][0];
}
int main () {
struct Matrix *a = create_matrix(3, 3);
struct Matrix *b;
read_matrix(a);
b = matrix_pow(a, 2);
print_matrix(b);
return 0;
}
/**
* Set command
*/
void command_set(const char* line) {
char cmd[MAX_BUFFER];
char key[MAX_BUFFER];
char func[MAX_BUFFER];
char arg1[MAX_BUFFER];
char arg2[MAX_BUFFER];
int argc = sscanf(line, "%s %s = %s %s %s", cmd, key, func, arg1, arg2);
if (argc < 3) {
puts("invalid arguments");
return;
}
uint32_t* matrix = NULL;
switch (argc) {
case 3:
if (strcasecmp(func, "identity") == 0) {
matrix = identity_matrix();
} else {
goto invalid;
}
break;
case 4:
if (strcasecmp(func, "random") == 0) {
uint32_t seed = atoll(arg1);
matrix = random_matrix(seed);
} else if (strcasecmp(func, "uniform") == 0) {
uint32_t value = atoll(arg1);
matrix = uniform_matrix(value);
} else if (strcasecmp(func, "cloned") == 0) {
MATRIX_GUARD(arg1);
matrix = cloned(m);
} else if (strcasecmp(func, "reversed") == 0) {
MATRIX_GUARD(arg1);
matrix = reversed(m);
} else if (strcasecmp(func, "transposed") == 0) {
MATRIX_GUARD(arg1);
matrix = transposed(m);
} else {
goto invalid;
}
break;
case 5:
if (strcasecmp(func, "sequence") == 0) {
uint32_t start = atoll(arg1);
uint32_t step = atoll(arg2);
matrix = sequence_matrix(start, step);
} else if (strcasecmp(func, "scalar#add") == 0) {
MATRIX_GUARD(arg1);
uint32_t value = atoll(arg2);
matrix = scalar_add(m, value);
} else if (strcasecmp(func, "scalar#mul") == 0) {
MATRIX_GUARD(arg1);
uint32_t value = atoll(arg2);
matrix = scalar_mul(m, value);
} else if (strcasecmp(func, "matrix#add") == 0) {
MATRIX_GUARD_PAIR(arg1, arg2);
matrix = matrix_add(m1, m2);
} else if (strcasecmp(func, "matrix#mul") == 0) {
MATRIX_GUARD_PAIR(arg1, arg2);
matrix = matrix_mul(m1, m2);
} else if (strcasecmp(func, "matrix#pow") == 0) {
MATRIX_GUARD(arg1);
uint32_t exponent = atoll(arg2);
matrix = matrix_pow(m, exponent);
} else {
goto invalid;
}
break;
}
entry* e = find_entry(key);
if (e == NULL) {
e = add_entry(key);
} else {
free(e->matrix);
}
e->matrix = matrix;
puts("ok");
return;
invalid:
puts("invalid arguments");
}