// O(s.length + ans.length)
function minimum_cycle(s){
  const L = s.length
  if(L <= 1) return s

  var i=0, j=1, cnt=0
  while(cnt < L){
    if(s[i] === s[j]){
      i = (i+1)%L
      j = (j+1)%L
      cnt++
    } else {
      j = (j+1)%L
      cnt = 0
    }
  }

  if(i < j) return s.slice(i,j)
  return s.slice(i) + s.slice(0,j)
}

console.log(cycle("101001101001101001101001")) // 110100
console.log(cycle("10111001001011100100")) // 0010010111
console.log(cycle("111000110010111000110010111000110010")) // 000110010111
console.log(cycle("1011101110111011101110111011")) // 0111