244 bytes

int[]f(int k,int t){int q,m,i,h,f,d[]=new int[k],b[]=d.clone();for(;t-->0;){q=k;d[q*=Math.random()]++;m=0;i=q;h=1;f=0;if(d[q]>1){for(;;){if(i<0){i=k-1;h=-1;}if(d[i%k]>0){m++;d[i%k]=0;}else{if(f>0)break;h*=-1;i=q;f=1;}i+=h;}b[m-1]++;}}return b;}


//

int[]f(int k,int t){
    int q,m,i,h,f,d[]=new int[k],b[]=d.clone();
    for(;t-->0;){
        q=k;d[q*=Math.random()]++;
        m=0;i=q;h=1;f=0;
        if(d[q]>1){
            for(;;){
                if(i<0){i=k-1;h=-1;}
                if(d[i%k]>0){m++;d[i%k]=0;}
                else{if(f>0)break;h*=-1;i=q;f=1;}
                i+=h;
            }
            b[m-1]++;
        }
    }
    return b;
}