CJam, 28 bytes (safe)
"jK=\~"5*)ib257b~{G$5$+}*]Jb
[Try it online][1].
Original output
7705397905065379035618588652533563996660018265606606763127193120855297133322151462150247488267491212817218321670720380456985476811737021068519164822984561148339610474891720342171053455881107227302663880445203851079295537592154028123394687360216561235621729967011148112746984677807932995700334185726563970223018774
Modified output
16650180159137697345989048346412185774444335111603430666402604460993564226370500963166158223117360250140073061887053326627468495236957122711656527124216908303912850181595147494475577084810653496778801228980874902968634143062
Solution
"jK=\~"5*Wcib257b~{G$5$+}*]Jb
[Try it online.][2]
How it works
I went a little overboard with this one...
The original code does the following:
"jK=\~"5* e# Push "jK=\~jK=\~jK=\~jK=\~jK=\~".
)i e# Pop the last character and cast it to integer.
b257b e# Convert the remainder of the string from that base to base 257.
~ e# Dump all resulting base-257 digits on the stack:
e# 137 72 124 88 81 145 85 32 28 251 118 230 53 13 245 147 256 116 187 22 224
{ e# Do the following 224 times:
G$5$+ e# Add copies of the 5th and 17th topmost integers on the stack
e# (recurrence of a lagged Fibonacci sequence).
}* e#
] e# Wrap the entire stack in an array.
Jb e# Convert from base 19 to integer.
e# The resulting integer is printed implicitly.
The intended change is replacing (i with Wci.
This leaves the repeated string untouched and pushes 65535 (as explained [here][3]by casting to an unsigned 16-bit character, then back to integer), so that the first elements of the lagged Fibonacci sequence become
87 225 162 210 73 196 142 219 175 61 40 147 0 93 75 55 103 116 237 188 108 122 176 133 135 240 251 155 224 82 181 75 23 87 139 49 148 169 84 109 110 166 52 103 83 185 78 73
and the loop is repeated 126 times.
[1]: http://cjam.aditsu.net/#code=%22jK%3D%5C~%225*)ib257b~%7BG%245%24%2B%7D*%5DJb [2]: http://cjam.aditsu.net/#code=%22jK%3D%5C~%225*Wcib257b~%7BG%245%24%2B%7D*%5DJb [3]: http://codegolf.stackexchange.com/a/54767