Hashing and Password Cracking

I was playing a game on cryptography where I encountered this problem:

Hashed Value of password: 24 109 76 35 22 94 83 25 106 104 73 87 56 38 56 50 10 92 58 84 44 88 24 112 125 121 125 43 122 55 106 54

The password is made of letters between 'f' and 'u'. The password is in alphabetical order. For hashing, the password is viewed as a sequence of numbers $x_1$, $x_2$, ..., $x_m$ in the field $F_{127}$. The $i^{th}$ number of the hashed sequence equals $x_1^{i-1} + x_2^{i-1}$ + ... + $x_m^{i-1}$. As we can see, there are 32 such numbers for i = 1 to 32."

My approach to the following problem is as follows:

• As there are 16 letters from f to u, each letter is mapped with integer 0 to 15.
• The length of the password is 24 as the first hashed value is 24 and hashing sequence for the same is $x_1^{0} + x_2^{0}$ + ... + $x_m^{0}$.
• The sum of the numbers from the integer mapped password mod 127 will be 109.
• Multiple equations can be formed like above.

Doing brute force to retrieve the password seems computationally infeasible. Is there a better approach to this problem?