Hi friends,please help me solve this if you have some spare time :)

a[1]-2*x[1]+x[n]=m;

a[2]-2*x[2]+x[1]=m;

a[3]-2*x[3]+x[2]=m;

. . .

a[n]-2*x[n]+x[n-1]=m;

here the array a is given and the constant m is also given,we have to find out the values of all the xi's in my approach i applied binary search on the value of x[n]..so lets suppose the assumed value of x[n]=mid then after solving the equation if i will get the value of x[n]>mid then i will reduce the mid,else increase the mid till the value of x[n] found out==mid...the problem here is that i have to find out an integral solution of the equations(if it exists)..so while solving the equations if some x[i] comes out to be a fractional value then we cannot proceed further with that value of mid..so if this happens then the current mid isnt a solution..now what should be the next mid value?increase/decrease or adjust it differently to converge to an integer solution(if it exists)?

last question:is there some other way in which this problem can be solved?