Vue add new value to array

I am new to VUE and for one project I am trying to update an array passing the object. I have two button which is called BUTTON 1 and BUTTON 2. If you click on BUTTON 1 then it will set an object to list[] using this.$set. But when BUTTON 2 is pressed it should update with the new value and should display as

{
 a:1,
 b:2,
 c:3
}

Right now I am using this.$set for button 2 as well and it removes the previous value then adds the new one as {c:3} only. Is there a way to add on value using VUE to display { a:1,b:2,c:3} when BUTTON 2 is clicked.

View

<div id="app">
  <button @click="button1()">Button 1</button>
  <button @click="button2()">Button 2</button>
</div>

Method

new Vue({
  el: "#app",
  data: {
    list:[]
  },
  methods: {
    
    button1(){
      var b = '0';
      this.$set(this.list, b, {
        1:{
            a: '1',
            b: '2'
        }
      })
      console.log(this.list);
    },
    
    button2(){
      var b = '0';
      this.$set(this.list, b,{
        1:{
            c: '3'
        }
      })
      console.log(this.list);
    },
    
  }
})

Below there is a jsfiddle link for my code

https://jsfiddle.net/ujjumaki/enj3dwo6/19/

Answer

Hope this works.

new Vue({
el: "#app",
data: {
list:[]
 },
 methods: {

button1(){
console.log('button 1');

const b = '0';
const restObj=this.list[b] && this.list[b][1]
    this.$set(this.list, b, {
    1:{
    ...restObj,
        a: '1',
        b: '2'
    }
  })
  
  console.log(this.list);
},

button2(){

const b = '0';
const restObj=this.list[b] && this.list[b][1]
    this.$set(this.list, b,{
    1:{
    ...restObj,
        c: '3'
    }
  })
  
  console.log(this.list);
},

}
})