#include<bits/stdc++.h>
using namespace std;
#define int long long
int t,n,m,k;
#define M 998244353
int jiecheng[200200];
int mypow(int a,int b){
    int ret=1;
    while(b){
        if(b&1)ret=ret*a%M;
        a=a*a%M;
        b/=2;
    }
    return ret;
}
int niyuan(int a){
    return mypow(a,M-2);
}
int zuhe(int a,int b){
    if(a<b)return 0;
    return jiecheng[a]*niyuan(jiecheng[b]*jiecheng[a-b]%M)%M;
}
int jia1,jian1;
int qry(int v){
    int jianab=v+jia1-jian1;
    if(jianab%2!=0)return 0;
    jianab/=2;
    int jiaab=m;
    if((jianab+jiaab)%2!=0)return 0;
    int a=(jianab+jiaab)/2,b=(jiaab-jianab)/2;
    int ret=zuhe(jia1,a)*zuhe(jian1,b)%M;
    //printf("%lld\n",ret);
    return ret;
}
signed main(){
    scanf("%lld",&t);
    jiecheng[0]=1;
    for(int i=1;i<200200;i++)
        jiecheng[i]=jiecheng[i-1]*i%M;
    while(t--){
        scanf("%lld%lld%lld",&n,&m,&k);
        jia1=0,jian1=0;
        int sum=n+m;
        jian1=sum/2;
        jia1=sum-jian1;
        printf("%lld\n",(qry(4*k-2)+qry(4*k-1)+qry(4*k)+qry(4*k+1))%M);
    }
    return 0;
}