Part of the answer uses GPT and GPT_Pro to solve the problem better. The reason is that they process data differently during execution. Let's look at the first way, which is to store ks+ in the ks array, and then go through each of the ks+, adding them up to get the final result:

```
int sum = 0;
for (int i = 0; i < ks.length; i++) {
sum += ks[i];
}
return sum;
```

The second rule is to add ks+ directly to get the final result:

```
int sum = 0;
for (int i = 0; i < ks.length; i++) {
sum += ks[i] + 1;
}
return sum;
```

It is worth noting that in the second notation, there is an extra step to add 1 to each term in ks+, which is why we get different results.

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