Parse nested digit-lead strings The task

A string S is constructed with the following process:


Start with S being the empty string.
Insert at some position of S a string of the form ds, where d is a nonzero digit and s is a string of d lowercase ASCII letters. We say ds is a constituent of S.
Go to step 2 or stop.


Your task is to take such a string as input, and output its constituents concatenated into a single string, in the order of appearance of their leading digits.
The output must be a single string, and there can't be any delimiters (including newlines) between the constituents.
You can choose whether the input and output strings have quotes.
Note that the input and output will never be empty.

Example

Let's construct a string with the above process.
The structure of the constituents is highlighted in the final result.

S = ""              // Insert "3abc"
S = "3abc"          // Insert "2gh" after 'a'
S = "3a2ghbc"       // Insert "1x" before '3'
S = "1x3a2ghbc"     // Insert "3tty" after '3'
S = "1x33ttya2ghbc" // Final result
     └┘│└┴┴┘│└┴┘││
       └────┴───┴┘


The output is obtained by concatenating the constituents in the order of their digits.
In this case, the correct output is

"1x3abc3tty2gh"


Rules and scoring

You can write a full program or a function.
the lowest byte count wins, and standard loopholes are disallowed.

Test cases

1k -&gt; 1k
4asdf -&gt; 4asdf
111xyz -&gt; 1z1y1x
8whatever3yes -&gt; 8whatever3yes
8what3yesever -&gt; 8whatever3yes
1x33ttya2ghbc -&gt; 1x3abc3tty2gh
63252supernestedstrings2ok -&gt; 6trings3eds2st5perne2su2ok
9long3yes4lo2ngwords11here -&gt; 9longrdsre3yes4lowo2ng1e1h
9abc8de7fg6hi5jk4lm3o2pq1rstuvwxyzabcdefghijklmnopqrst -&gt; 9abcopqrst8deijklmn7fgdefgh6hizabc5jkwxy4lmuv3ost2pq1r
JavaScript (ES6), 68 bytes

f=s=&gt;s&amp;&amp;f(s.replace(/\d\D+$/,m=&gt;(s=m.slice(0,i=++m[0]),m.slice(i))))+s


Explanation

Based on a simple concept:


Match the last digit n followed by n letters in the input string
Remove it from the input string and add it to the start of the output string
Repeat until the input string is empty


Recursion was the shortest way to do this in JavaScript.



f=s=&gt;
  s&amp;&amp;                        // if the input string is empty, return the empty string
  f(                         // prepend the constituent before it
    s.replace(/\d\D+$/,m=&gt;(  // match the last digit followed by every remaining letter
      s=m.slice(0,n=++m[0]), // set s to the constituent (n followed by n letters)
                             // (we must use s because it is our only local variable)
      m.slice(n)             // replace the match with only the letters after it
    ))
  )+s                        // append the constituent
&lt;input type="text" id="input" value="9long3yes4lo2ngwords11here" /&gt;
&lt;button onclick="result.textContent=f(input.value)"&gt;Go&lt;/button&gt;
&lt;pre id="result"&gt;&lt;/pre&gt;