A little understanding of LCT

It's really worthless
After the boss finished talking about the basics of LCT, Gao asked a question. as follows.

The cut operation was originally like this

void cut(int x,int y)
{
    makeroot(x);
    ac(y);
    putdown(x);
    splay(y);     <<<<<<<这里
    putdown(y);
    par[ls[y]]=fa[ls[y]]=0;
    lson[y]=0;
}

But as the arrow points, why splay this point?

After modification, it looks like this:

void cut(int x,int y)
{
    makeroot(x);
    ac(y);
    putdown(x);
    par[y]=fa[y]=0;
    rson[x]=0;
}

It feels like it's okay, because x, y are connected.
past the example. submit.

Then it's RE. For the original function, you can AC.
why?I feel so retarded.
"x, y are connected." That's the problem.

for example. A splay (auxiliary tree) is shown in the figure, the red is the x point. Actually point y (blue) is in the right subtree of point x, not the right child.
Think carefully, since this splay tree is built with depth as the key, then the y point should be the successor and not the son of the x point.
In short, in splay (auxiliary tree), the two points x and y are not connected. I can pass the sample only because the sample is too watery, and the successor is the right son. . .