#include <bits/stdc++.h>
using namespace std;
const int maxN = 250001, maxTreeSize = 1 << 19;
const long long INF = 1000000000000000000LL;//10^18
struct Tree
{
int T[maxTreeSize], offset;
void resize(int n)
{
for (offset = 1; offset < n; offset *= 2);
for (int i=offset; i<offset+n; i++)
T[i] = 1;
for (int i=offset-1; i>0; i--)
T[i] = T[i * 2] + T[i*2+1];
}
int query(int a)
{
int left = offset, right = offset * 2, v = 1;
while (v < offset)
{
if (a <= T[v * 2])
v *= 2;
else
a -= T[v * 2], v = v*2+1;
}
int res = v - offset + 1;
for (; v > 0; v /= 2)
T[v]--;
return res;
}
} tree;
vector <long long> a[maxN];
long long npo2(int n)
{ return 1LL * n * (n - 1) / 2; }
long long get_a(int n, long long k)
{
if (k < 0 or k > npo2(n)) return 0;
k = min(k, npo2(n) - k);
if (k >= a[n].size()) return INF;
return a[n][k];
}
int main()
{
a[0].push_back(1);
a[1].push_back(1);
int n;
long long k;
scanf ("%d%lld", &n, &k);
for (int i=2; i<=n; i++)
{
a[i].resize(i < 3000 ? 100 : 7);
a[i][0] = 1;
long long s = npo2(i)/2+1;
for (int j=1; j<s; j++)
{
a[i][j] = a[i][j - 1] + get_a(i - 1, j) - get_a(i - 1, j - i);
if (a[i][j] >= INF)
{
a[i].resize(j);
break;
}
}
}
if ((n & 2) or get_a(n, npo2(n)/2) < k)
{
printf("NIE\n");
return 0;
}
printf("TAK\n");
long long invs = npo2(n) / 2;
tree.resize(n);
for (int i=1; i<=n; i++)
{
long long v = 0;
for (int j=max(1LL, invs+1 - npo2(n-i)); true; j++)
{
long long d = get_a(n - i, invs - (j - 1));
if (k <= v + d)
{
printf("%d ", tree.query(j));
k -= v;
invs -= j - 1;
break;
}
v += d;
}
}
printf("\n");
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 | #include <bits/stdc++.h> using namespace std; const int maxN = 250001, maxTreeSize = 1 << 19; const long long INF = 1000000000000000000LL;//10^18 struct Tree { int T[maxTreeSize], offset; void resize(int n) { for (offset = 1; offset < n; offset *= 2); for (int i=offset; i<offset+n; i++) T[i] = 1; for (int i=offset-1; i>0; i--) T[i] = T[i * 2] + T[i*2+1]; } int query(int a) { int left = offset, right = offset * 2, v = 1; while (v < offset) { if (a <= T[v * 2]) v *= 2; else a -= T[v * 2], v = v*2+1; } int res = v - offset + 1; for (; v > 0; v /= 2) T[v]--; return res; } } tree; vector <long long> a[maxN]; long long npo2(int n) { return 1LL * n * (n - 1) / 2; } long long get_a(int n, long long k) { if (k < 0 or k > npo2(n)) return 0; k = min(k, npo2(n) - k); if (k >= a[n].size()) return INF; return a[n][k]; } int main() { a[0].push_back(1); a[1].push_back(1); int n; long long k; scanf ("%d%lld", &n, &k); for (int i=2; i<=n; i++) { a[i].resize(i < 3000 ? 100 : 7); a[i][0] = 1; long long s = npo2(i)/2+1; for (int j=1; j<s; j++) { a[i][j] = a[i][j - 1] + get_a(i - 1, j) - get_a(i - 1, j - i); if (a[i][j] >= INF) { a[i].resize(j); break; } } } if ((n & 2) or get_a(n, npo2(n)/2) < k) { printf("NIE\n"); return 0; } printf("TAK\n"); long long invs = npo2(n) / 2; tree.resize(n); for (int i=1; i<=n; i++) { long long v = 0; for (int j=max(1LL, invs+1 - npo2(n-i)); true; j++) { long long d = get_a(n - i, invs - (j - 1)); if (k <= v + d) { printf("%d ", tree.query(j)); k -= v; invs -= j - 1; break; } v += d; } } printf("\n"); return 0; } |
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