<p>Given two strings&nbsp;<code>s</code>&nbsp;and&nbsp;<code>t</code>, your goal is to convert&nbsp;<code>s</code>&nbsp;into&nbsp;<code>t</code>&nbsp;in&nbsp;<code>k</code><strong>&nbsp;</strong>moves or less.</p>

<p>During the&nbsp;<code>i<sup>th</sup></code>&nbsp;(<font face="monospace"><code>1 &lt;= i &lt;= k</code>)&nbsp;</font>move you can:</p>

<ul>
	<li>Choose any index&nbsp;<code>j</code>&nbsp;(1-indexed) from&nbsp;<code>s</code>, such that&nbsp;<code>1 &lt;= j &lt;= s.length</code>&nbsp;and <code>j</code>&nbsp;has not been chosen in any previous move,&nbsp;and shift the character at that index&nbsp;<code>i</code>&nbsp;times.</li>
	<li>Do nothing.</li>
</ul>

<p>Shifting a character means replacing it by the next letter in the alphabet&nbsp;(wrapping around so that&nbsp;<code>&#39;z&#39;</code>&nbsp;becomes&nbsp;<code>&#39;a&#39;</code>). Shifting a character by&nbsp;<code>i</code>&nbsp;means applying the shift operations&nbsp;<code>i</code>&nbsp;times.</p>

<p>Remember that any index&nbsp;<code>j</code>&nbsp;can be picked at most once.</p>

<p>Return&nbsp;<code>true</code>&nbsp;if it&#39;s possible to convert&nbsp;<code>s</code>&nbsp;into&nbsp;<code>t</code>&nbsp;in no more than&nbsp;<code>k</code>&nbsp;moves, otherwise return&nbsp;<code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;input&quot;, t = &quot;ouput&quot;, k = 9
<strong>Output:</strong> true
<b>Explanation: </b>In the 6th move, we shift &#39;i&#39; 6 times to get &#39;o&#39;. And in the 7th move we shift &#39;n&#39; to get &#39;u&#39;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;abc&quot;, t = &quot;bcd&quot;, k = 10
<strong>Output:</strong> false
<strong>Explanation: </strong>We need to shift each character in s one time to convert it into t. We can shift &#39;a&#39; to &#39;b&#39; during the 1st move. However, there is no way to shift the other characters in the remaining moves to obtain t from s.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aab&quot;, t = &quot;bbb&quot;, k = 27
<strong>Output:</strong> true
<b>Explanation: </b>In the 1st move, we shift the first &#39;a&#39; 1 time to get &#39;b&#39;. In the 27th move, we shift the second &#39;a&#39; 27 times to get &#39;b&#39;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length, t.length &lt;= 10^5</code></li>
	<li><code>0 &lt;= k &lt;= 10^9</code></li>
	<li><code>s</code>, <code>t</code> contain&nbsp;only lowercase English letters.</li>
</ul>

class Solution:
    def canConvertString(self, s: str, t: str, k: int) -> bool:
        # we know k can be large, but think of each slot in
        # the modular ring, think about all of the differences
        # of some char (i.e. c->g), there is a collection of
        # revolutions on this ring to do so. if we have enough!
        # use it! if not it's impossible. we live in q land
        # which is 26. 
        if len(s) != len(t):
            return False
        q = 26
        baseCountOnAllSlots = (k+1) // q
        remainder = (k+1) % q
        countOnSlotRing = [baseCountOnAllSlots] * 26
        for slot in range(remainder):
            countOnSlotRing[slot]+=1
        print(countOnSlotRing, 'is the counts!')
        for a, b in zip(s,t):
            if a != b:
                slot = (((ord(b) - ord(a)) % q) + q) % q 
                countOnSlotRing[slot] -=  1
                if countOnSlotRing[slot] < 0:
                    return False
        return True
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