Calculate combinations in MIPS - c

Question

I am working on a program that calculates combinations in MIPS. The user enters the size of the pool, and number of balls to pick from it, and the program should output the total combinations. The program correctly calculates the numerator, but when it comes to dividing the numerator (n!) by the denominator, which is also correctly calculated, the combinations number is wrong.
I think something goes wrong with $t2 when it is used in main, but not sure what exactly or how to fix it.
.data
message1: .asciiz "Enter input for the size of the large pool: "
message2: .asciiz "Enter input for # of balls to be selected from large pool: "
message5: .asciiz "The numerator is: "
newline: .asciiz "\n"
.text
.globl main
main:
# Call on function messages
jal messages
# Calculate factrl for # from large pool size
move $a0, $s2
jal factrl # Call on factrl function
move $t5, $v0
# Find (n-k) for large pool
sub $t0, $s1, $s2
# Intialize $t2 to 1
li $t2, 1
# Call function while for large pool
move $a1, $s1
move $a2, $t0
jal while
move $v0, $t2
# Find probability for large
move $a0, $v0
move $a1, $t0
jal combination
move $t7 $v0
li $v0, 4
la $a0, newline
syscall
li $v0, 1
add $t7, $t7, $zero
syscall
# Exit Program
li $v0, 10
syscall
messages:
# Request size of large pool
li $v0, 4
la $a0, message1
syscall
# Get input for size of large pool
li $v0, 5
syscall
# Store input in register
move $s1, $v0
# Request # selected from large pool
li $v0, 4
la $a0, message2
syscall
# Get input for # of large pool
li $v0, 5
syscall
# Store input in register
move $s2, $v0
li $v0, 4
la $a0, newline
syscall
jr $ra
factrl:
sw $ra, 4($sp) # save the return address
sw $a0, 0($sp) # save the current value of n
addi $sp, $sp, -8 # move stack pointer
slti $t0, $a0, 2 # save 1 iteration, n=0 or n =1; n!=1
beq $t0, $zero, L1 # not less than 2 , calculate n(n - 1)!
addi $v0, $zero, 1 # n=1; n!=1
jr $ra # now multiply
L1:
addi $a0, $a0, -1 # n = n - 1
jal factrl # now (n - 1)!
addi $sp, $sp, 8 # reset the stack pointer
lw $a0, 0($sp) # fetch saved (n - 1)
lw $ra, 4($sp) # fetch return address
mul $v0, $a0, $v0 # multiply (n)*(n - 1)
jr $ra # return value n!
while:
addi $sp, $sp, -8 # allocate space in stack
sw $ra, 4($sp)
sw $a1, 0($sp) # store the value of $s1 on the stack
beq $a1, $a2, numerator
mult $t2, $a1 # multiply val x n
mflo $t3
move $t2, $t3
addi $a1, $a1, -1 # n = n-1
j while
numerator:
li $v0, 4
la $a0, message5
syscall
# Print the numerator
li $v0, 1
move $a0, $t2
syscall
lw $a1, 0($sp)
addi $sp, $sp, 8 # reset stack pointer
jr $ra
combination:
div $v0, $a1, $a0
jr $ra
exit:
li $v0, 10
syscall