postfix to infix

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Problem

Convert from postfix (reverse polish notation) to minimally parenthesized infix notation. * and / are higher precedence than + and -. * and + are associative while - and / are not.

abc+- -> a-(b+c)
abc++ -> a+b+c, not a+(b+c) because associativity.
ab+c* -> (a+b)*c
ab*c+ -> a*b+c, parenthesis not needed due to higher precedence.

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exec is denied

now post-mortem time, all source codes will be revealed

Sample input:_

abc+-
abc++
ab+c*
ab*c+

Sample output:

a-(b+c)
a+b+c
(a+b)*c
a*b+c

Sample input:_

kr/vgop*d*q/lzn*+hy/w*-j-x+ia*+c*s+*m//b/*u/e-f-/
ug*i*d*b/h*zel*c-*w+q*av/-/f*
an/e/dyb/p*ks/w/mvj/i//t*/**qg/-*c/r*
alfb*r*h*n*q/so/vc*t*--*x*d+i/j//
imyq*o*g/w/r/k-/un*+bxf/lae/-j/**+/t*d*ch*-
ktx/ej/a*d/r*m*i-n*f*qhvc*lo+*-*g*-/us*p*+/
ftvj/cy*glmzi*qd*x***o/-/n-p-b-/e/**k+uw*+ha*-/
in*p*v/j/x*ub*qrht/a/lcef/++k-/z//-*yo/+ds/-/g-m-
dzf/r/pl*emiw/h*k*xc/g+/*-o+n-/*j/*b/
bp/tva/y*ej*m/sz/r-hn-+-/u*i/*d+*
ad/v*l*ey/x/qz/s-*p/j//
ba/vwg*i/q*j/lc-*dym/f*/o+p+s*-//x/r-

Sample output:

k/r/(v*g/(o*p*d/q*((l+z*n-h/y*w-j+x+i*a)*c+s)/m)/b/u-e-f)
u*g*i*d/b*h/((z*(e*l-c)+w)*q-a/v)*f
a/n/e*(d*y/b*p*k/s/w/(m/(v/j/i)*t)-q/g)/c*r
a/((l*(f*b*r*h*n/q-(s/o-v*c*t))*x+d)/i/j)
i/(m/(y*q*o/g/w/r-k)+u*n+b*x/f*(l-a/e)/j)*t*d-c*h
k/(t/x/((e/j*a/d*r*m-i)*n*f-q*(h-v*c*(l+o))*g)+u*s*p)
f/(t*v/j*c*y/(g/(l-m*z*i*q*d*x/o)-n-p-b)/e+k+u*w-h*a)
i*n*p/v/j*x/(u*b*(q-r/(h/t/a/(l+c+e/f-k)/z))+y/o-d/s)-g-m
d*z/f/r*p*l/(e-m*i/w*h*k/(x/c+g)+o-n)/j/b
b/p*(t*v/a*y/(e*j/m-(s/z-r+h-n))*u/i+d)
a/d*v*l/(e/y/x*(q/z-s)/p/j)
b/a/(v/(w*g/i*q/j*(l-c)-(d/(y/m*f)+o+p)*s))/x-r

Sample input:_

mk/fr/q/o*i/x/c/hun-vg*b/+w-e-lz*-/-sa*-/tj*+
mk*ld/vw*zi/h+/s/x*//
cq*t/nv/e/f*m*h/s/a-/p*xg*ybz*ojd*l//*/r/+w*+
dx/m/b*q*n*u/r/wy/ok+zc/p*+f/-ea/-/
gh*kf*v/zt*l*yx*s/o*imq/aw*uc*d**+/*p/j*-*/r-
mn*w*oua/q*d+f+/ph*r*-ci*+*k/b+s+
jxh/za*p*f*t*ou/q**wi*r*c*b//*e//d-
yj*u/kwng*d*vo/q/*rhs/f/z*-*tm*+*/e//
wn/vqa/f/j/xt*b*yl/p/k*d-u+e/*m/g*+/or*i/c//s-*h/z-
jzc*p*i*ox/hg*t/ae/b/ny-*--*l*k*s+v+d*w*/
yuv*hb*e*i/j*/f**k*g*
uo*ry/e*ps*h/b*j-*d*lf/+*i-

Sample output:

m/k/(f/r/q*o/i/x/c-h/(u-n+v*g/b-w-e-l*z)-s*a)+t*j
m*k/(l/d/(v*w/(z/i+h)/s*x))
c*q/t/(n/v/e*f*m/h/s-a)*p+(x*g+y/(b*z*o/(j*d/l))/r)*w
d/x/m*b*q*n/u/r/(w/y-(o+k+z/c*p)/f-e/a)
g*h/(k*f/v*(z*t*l-y*x/s*o*i/(m/q+a*w*u*c*d)/p*j))-r
m*n*w*(o/(u/a*q+d+f)-p*h*r+c*i)/k+b+s
j/(x/h*z*a*p*f*t*o/u*q/(w*i*r*c/b)/e)-d
y*j/u/(k/(w*(n*g*d*v/o/q*(r-h/s/f*z)+t*m))/e)
w/n*(v/(q/a/f/j+x*t*b*(y/l/p*k-d+u)/e/m*g)/(o*r/i/c)-s)/h-z
j/((z*c*p*i*(o/x-(h*g/t-a/e/b*(n-y)))*l*k+s+v)*d*w)
y*u*v/(h*b*e/i*j)*f*k*g
u*o*(r/y*e*(p*s/h*b-j)*d+l/f)-i

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