P3048.cpp

#include <iostream>
using namespace std;
int n, k, flag;
int main()
{
    scanf("%d%d", &n, &k);
    if (k == 1)
    {
        printf("%c", '1');
        for (int i = 2; i <= n; i++)
            printf("%c", '0');
    }
    else if (k == 2)
    {
        int s = 0, i = 1;
        for (i = 1; s < n; i++)
            s += i;
        i--, s -= i;
        putc('1', stdout);
        for (int j = 1; j <= i; j++)
            printf("%c", (i + 1 - n + s == j) + '0');
    }
    else if (k == 3)
    {
        int s = 0, i = 2;
        for (i = 2; s < n; i++)
            s += i * (i - 1) / 2;
        i--, s -= i * (i - 1) / 2;
        int nn = n - s, ns = 0, j = 1;
        for (j = 1; ns < nn; j++)
            ns += j;
        j--, ns -= j;
        putc('1', stdout);
        for (int k = 1; k <= i - j - 1; k++)
            printf("%c", '0');
        putc('1', stdout);
        for (int k = 1; k <= j; k++)
            printf("%c", (j + 1 - nn + ns == k) + '0');
    }
    else
    {
        unsigned long long x = (1ULL << k) - 1ULL, t;
        for (int i = 2; i <= n; i++)
        {
            t = x + (x & -x);
            x = t | ((((t & -t) / (x & -x)) >> 1ULL) - 1ULL);
        }
        for (int i = 63; i >= 0; i--)
        {
            if (x & (1ULL << i))
                flag = 1;
            if (flag)
            {
                printf("%c", char(((x >> i) & 1ULL) + '0'));
            }
        }
        printf("\n");
    }
}