#include<stdio.h>
long long a[65537];
int bsearch(int b,int t,long long k)
{
    int mid=(b+t)/2;
    if(b>t)
    {
        return 0;
    }
    if(k>a[mid])
    {
        bsearch(mid+1,t,k);
    }
    else if(k<a[mid])
    {
        bsearch(b,mid-1,k);
    }
    else return 1;
}
void main()
{
    int n;
    long long k,i;
    scanf("%d",&n);
    for(i=1;i<=65536;i++)
    {
        a[i]=i*(i-1)/2+1;
    }
    while(n>0)
    {
        scanf("%lld",&k);
        printf("%d",bsearch(1,65536,k));
        if(n!=1)
            printf(" ");
        n--;
    }
}

I don't know your mistake. But I can tell you that you can find out if the given k is really 1 without binary search. It's just a simple math. It's a formula and you know the formula.
k = x (x - 1) / 2 + 1 just find x and make sure that it has an positive integer value. good luck

thanks