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berlekamp_massey.cpp
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berlekamp_massey.cpp
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// BOJ 10562 나이트
#include <bits/stdc++.h>
#define sz size()
#define bk back()
#define fi first
#define se second
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const int MOD = 1e9 + 9;
ll ipow(ll base, ll exp) {
ll ret = 1;
while (exp) {
if (exp & 1)
ret = ret * base % MOD;
base = base * base % MOD;
exp >>= 1;
}
return ret;
}
vector<int> berlekamp_massey(vector<int> &x) {
vector<int> ls, cur;
int lf, ld;
for (int i = 0; i < x.sz; i++) {
ll t = 0;
for (int j = 0; j < cur.sz; j++)
t = (t + (ll)x[i - j - 1] * cur[j]) % MOD;
if ((t - x[i]) % MOD == 0)
continue;
if (cur.empty()) {
cur.resize(i + 1);
lf = i;
ld = (t - x[i]) % MOD;
continue;
}
ll k = (t - x[i]) * ipow(ld, MOD - 2) % MOD;
vector<int> c(i - lf - 1);
c.push_back(k);
for (auto &j : ls)
c.push_back(-j * k % MOD);
if (c.sz < cur.sz)
c.resize(cur.sz);
for (int j = 0; j < cur.sz; j++)
c[j] = (c[j] + cur[j]) % MOD;
if (i - lf + (int)ls.sz >= (int)cur.sz)
tie(ls, lf, ld) = make_tuple(cur, i, (t - x[i]) % MOD);
cur = c;
}
for (auto &i : cur)
i = (i % MOD + MOD) % MOD;
return cur;
}
int get_nth(vector<int> &rec, vector<int> &dp, ll n) {
int m = rec.sz;
vector<int> s(m), t(m);
s[0] = 1;
if (m != 1)
t[1] = 1;
else
t[0] = rec[0];
auto mul = [&rec](vector<int> v, vector<int> w) {
int m = v.sz;
vector<int> t(2 * m);
for (int j = 0; j < m; j++) {
for (int k = 0; k < m; k++) {
t[j + k] += (ll)v[j] * w[k] % MOD;
if (t[j + k] >= MOD)
t[j + k] -= MOD;
}
}
for (int j = 2 * m - 1; j >= m; j--) {
for (int k = 1; k <= m; k++) {
t[j - k] += (ll)t[j] * rec[k - 1] % MOD;
if (t[j - k] >= MOD)
t[j - k] -= MOD;
}
}
t.resize(m);
return t;
};
while (n) {
if (n & 1)
s = mul(s, t);
t = mul(t, t);
n >>= 1;
}
ll ret = 0;
for (int i = 0; i < m; i++)
ret = (ret + (ll)s[i] * dp[i] % MOD) % MOD;
return ret;
}
int guess_nth_term(vector<int> &v, vector<int> &x, ll n) {
if (n < x.sz)
return x[n];
return get_nth(v, x, n);
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
vector<vector<vector<int>>> dp(5);
for (int i = 2; i <= 4; i++) {
dp[i].resize(105);
int k = 1 << (2 * i);
for (int n = 0; n < 105; n++)
dp[i][n].resize(k);
}
for (int j = 0; j < 16; j++)
dp[2][2][j] = 1;
for (int n = 3; n < 100; n++) {
for (int i = 0; i < 16; i++) {
ll k = 0;
for (int j = 0; j < 16; j++) {
if ((i & 1) && (j & 8))
continue;
if ((i & 2) && (j & 4))
continue;
if (!(i & 4) != !(j & 1))
continue;
if (!(i & 8) != !(j & 2))
continue;
k += dp[2][n - 1][j];
}
dp[2][n][i] = k % MOD;
}
}
for (int i = 0; i < 64; i++) {
if ((i & 1) && (i & 32))
continue;
if ((i & 4) && (i & 8))
continue;
dp[3][2][i] = 1;
}
for (int n = 3; n < 100; n++) {
for (int i = 0; i < 64; i++) {
if ((i & 1) && (i & 32))
continue;
if ((i & 4) && (i & 8))
continue;
ll k = 0;
for (int j = 0; j < 64; j++) {
if ((i & 1) && (j & 16))
continue;
if ((i & 2) && (j & 8))
continue;
if ((i & 2) && (j & 32))
continue;
if ((i & 4) && (j & 16))
continue;
if ((i & 8) && (j & 32))
continue;
if ((i & 32) && (j & 8))
continue;
if (!(i & 8) != !(j & 1))
continue;
if (!(i & 16) != !(j & 2))
continue;
if (!(i & 32) != !(j & 4))
continue;
k += dp[3][n - 1][j];
}
dp[3][n][i] = k % MOD;
}
}
for (int i = 0; i < 256; i++) {
if ((i & 1) && (i & 64))
continue;
if ((i & 2) && (i & 128))
continue;
if ((i & 4) && (i & 16))
continue;
if ((i & 8) && (i & 32))
continue;
dp[4][2][i] = 1;
}
for (int n = 3; n < 100; n++) {
for (int i = 0; i < 256; i++) {
if ((i & 1) && (i & 64))
continue;
if ((i & 2) && (i & 128))
continue;
if ((i & 4) && (i & 16))
continue;
if ((i & 8) && (i & 32))
continue;
ll k = 0;
for (int j = 0; j < 256; j++) {
if ((i & 1) && (j & 32))
continue;
if ((i & 2) && (j & 16))
continue;
if ((i & 2) && (j & 64))
continue;
if ((i & 4) && (j & 32))
continue;
if ((i & 4) && (j & 128))
continue;
if ((i & 8) && (j & 64))
continue;
if ((i & 16) && (j & 64))
continue;
if ((i & 32) && (j & 128))
continue;
if ((i & 64) && (j & 16))
continue;
if ((i & 128) && (j & 32))
continue;
if (!(i & 16) != !(j & 1))
continue;
if (!(i & 32) != !(j & 2))
continue;
if (!(i & 64) != !(j & 4))
continue;
if (!(i & 128) != !(j & 8))
continue;
k += dp[4][n - 1][j];
}
dp[4][n][i] = k % MOD;
}
}
vector<vector<int>> v(5);
for (int i = 2; i <= 4; i++) {
v[i].push_back(1 << i);
for (int n = 2; n < 100; n++) {
ll k = 0;
for (int j = 0; j < dp[i][n].sz; j++)
k += dp[i][n][j];
v[i].push_back(k % MOD);
}
}
vector<vector<int>> bm(5);
for (int i = 2; i <= 4; i++)
bm[i] = berlekamp_massey(v[i]);
int t;
cin >> t;
while (t--) {
int m, n;
cin >> m >> n;
if (m == 1)
cout << ipow(2, n) << '\n';
else
cout << get_nth(bm[m], v[m], n - 1) << '\n';
}
}