We have numbers from $$$\ a_1, \ldots, a_n$$$, where each number is between $$$(0 \leq a_i < 2^k)$$$. We're trying to find a sequence of these numbers $$$(1 \leq i_1 < i_2 < \ldots < i_T \leq n)$$$ , where $$$T$$$ is $$$(T \geq 1)$$$ , and when we combine them using XOR $$$(a_{i_1} \oplus \ldots \oplus a_i)$$$, the result is $$$0$$$. This problem is well-known and can be solved using Gaussian Elimination technique($$$\mathcal{O}(\frac{nk^2}{w} + \frac{k^3}{w})$$$) in $$$(O(k^2))$$$ time.

But what if we want to find the smallest number of elements $$$T$$$ (still with $$$(T \geq 1.)$$$)? So far, I've only thought of a method that takes about $$$(O^*(n^k))$$$ time by trying all subsets with sizes up to $$$k$$$ and checking if their XOR sum is $$$0$$$.

Can we find a faster way, maybe something like $$$(O(\text{polylog}(n, k)))$$$? Any help would be appreciated, thank you.

In every contest, we meet new people, work with teammates, and sometimes even compete against our friends. But what’s amazing is the bond we form through these experiences.

At ICPC, it’s not just about winning; it’s also about the laughs we share when a problem stumps us all, the collective sigh of relief when we finally solve a tough challenge, and the excitement of learning from each other. These moments create friendships that last long after the contest ends.

So let’s cherish these connections because they are truly the best part of ICPC contests.

Picture- $$$47$$$ $$$Contest$$$ — $$$North$$$ $$$America$$$ $$$Champion$$$ #icpcwfluxor

$$$University$$$ $$$of$$$ $$$Waterloo$$$ $$$(47133)$$$

$$$A$$$ $$$proper$$$ $$$congratulations$$$ $$$is$$$ $$$well$$$ $$$deserved!$$$ $$$Just$$$ $$$Look$$$ $$$At$$$ $$$the$$$ $$$Legendary$$$ $$$Coach$$$ Errichto

$$$47$$$ $$$Contest$$$ — $$$Europe$$$ $$$Champion$$$

$$$Harbour$$$.$$$Space$$$ $$$University$$$ $$$(47034)$$$

$$$46$$$ $$$Contest$$$ — $$$WORLD$$$ $$$CHAMPION$$$

$$$1$$$ $$$Peking$$$ $$$University$$$ $$$(46069)$$$

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In a 4-hour contest (Google Code Jam 2018 Final), he had 0 points for 3 hours and 45 minutes, and was at the bottom of the rank list.

But in the last 15 minutes something happened that he took the second position at once. How?

He was trying to target the most difficult problem and the 15th, I repeat, 15th submission was accepted as it was accepted and the Legend came up next to the tourist !

Risk is one such thing, which if missed is a big loss, but if taken, unimaginable results are at hand. But that risk must be calculated, time and energy must be invested behind it, there must be a promise not to give up, and there must be a mindset to accept the results...

Contests can have last-minute twists as if it is simulating real life.

Errichto is addressed as "Sir" by many in the coding community. He truly deserves the title "Sir".

Hi everyone!

I think it would be better if Codeforces displays contest performance rating along with rating change, similar to Atcoder.

I urge everyone to refrain from discussing cheaters and alternate accounts, and instead focus on creating meaningful and constructive blogs. Such discussions are not conducive to our community's atmosphere. For examples this blog-

Blog

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It's comments-

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It's a humble request to everyone, instead of exposing others or focusing on cheaters, we should trying focusing on self-improvement.

Thanks!